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Journal of Computer-Generated Euclidean Geometry |
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Circumcenter Deko Dekov
Circumcenter = Orthocenter of the Medial Triangle. Circumcenter = Nine-Point Center of the
Excentral Triangle. Circumcenter = Nine-Point Center of the
Anticomplementary Triangle. Circumcenter = Orthocenter of the Pedal Triangle
of the Circumcenter. Circumcenter = Nine-Point Center of the
Antipedal Triangle of the Incenter. Circumcenter = Nine-Point Center of the
Antipedal Triangle of the Orthocenter. Circumcenter = Centroid of the Antipedal
Triangle of the Symmedian Point. Circumcenter = Brocard Midpoint of the Antipedal
Triangle of the First Brocard Point. Circumcenter = Brocard Midpoint of the Antipedal
Triangle of the Second Brocard Point. Circumcenter = de Longchamps Point of the Euler
Triangle. Circumcenter = Tarry Point of the First Brocard
Triangle. Circumcenter = Center of the Outer Soddy Circle
of the Lucas Central Triangle. Circumcenter = Nine-Point Center of the Hexyl
Triangle. Circumcenter = Orthocenter of the Johnson
Triangle. Circumcenter = Inner Napoleon Point of the Outer
Fermat Triangle. Circumcenter = Inner Napoleon Point of the Inner
Fermat Triangle. Circumcenter = Inner Vecten Point of the Outer
Vecten Triangle. Circumcenter = Inner Vecten Point of the Inner
Vecten Triangle. Circumcenter = Tarry Point of the Inner Gallatly-Kiepert
Triangle. For any Triangle Center, the Circumcenter is the
Circumcenter of the Circumcevian Triangle of the Triangle Center. Circumcenter = Inner Lemoine-Kiepert Point of
the First Brocard Triangle. Circumcenter = Inner 36º Kiepert Point of
the Outer Pentagon Triangle. Circumcenter = Inner 36º Kiepert Point of
the Inner Pentagon Triangle. Circumcenter = Inner 22.5º Kiepert Point of
the Outer Octagon Triangle. Circumcenter = Outer 22.5º Kiepert Point of
the Inner Octagon Triangle. Circumcenter = Inner 18º Kiepert Point of
the Outer Decagon Triangle. Circumcenter = Outer 18º Kiepert Point of
the Inner Decagon Triangle. Circumcenter = Inner 15º Kiepert Point of
the Outer 15-gon Triangle. Circumcenter = Outer 15º Kiepert Point of
the Inner 15-gon Triangle. Circumcenter = Inner Lemoine-Kiepert Point of
the Inner Gallatly-Kiepert Triangle. Circumcenter = Center of the Circumcircle. Circumcenter = Center of the Second Droz-Farny
Circle. Circumcenter = Center of the First Droz-Farny
Circle of the Medial Triangle. Circumcenter = Center of the First Droz-Farny
Circle of the Cevian Triangle of the Tarry Point. Circumcenter = Center of the First Droz-Farny
Circle of the Cevian Triangle of the Steiner Point. Circumcenter = Center of the First Droz-Farny
Circle of the Cevian Triangle of the Kiepert-Parry Point. Circumcenter = Center of the First Droz-Farny
Circle of the Cevian Triangle of the Parry Point. Circumcenter = Center of the Nine-Point Circle
of the Excentral Triangle. Circumcenter = Center of the Nine-Point Circle
of the Anticomplementary Triangle. Circumcenter = Center of the First Droz-Farny
Circle of the Pedal Triangle of the Circumcenter. Circumcenter = Center of the Nine-Point Circle
of the Antipedal Triangle of the Incenter. Circumcenter = Center of the Nine-Point Circle
of the Antipedal Triangle of the Orthocenter. Circumcenter = Center of the Moses Circle of the
Antipedal Triangle of the First Brocard Point. Circumcenter = Center of the Half-Moses Circle
of the Antipedal Triangle of the First Brocard Point. Circumcenter = Center of the Moses Circle of the
Antipedal Triangle of the Second Brocard Point. Circumcenter = Center of the Half-Moses Circle
of the Antipedal Triangle of the Second Brocard Point. Circumcenter = Center of the Outer Soddy Circle
of the Lucas Central Triangle. Circumcenter = Center of the Nine-Point Circle
of the Hexyl Triangle. Circumcenter = Center of the First Droz-Farny
Circle of the Johnson Triangle. Circumcenter = Center of the Outer Apollonius
Circle of the Lucas Circles. Circumcenter = Center of the Inner Apollonius
Circle of the Excircles of the Excentral Triangle. Circumcenter = Center of the Inner Apollonius
Circle of the Excircles of the Anticomplementary Triangle. Circumcenter = Center of the Inner Apollonius
Circle of the Excircles of the Antipedal Triangle of the Incenter. Circumcenter = Center of the Inner Apollonius
Circle of the Excircles of the Antipedal Triangle of the Orthocenter. Circumcenter = Center of the Inner Apollonius
Circle of the Excircles of the Hexyl Triangle. Circumcenter = Center of the Gallatly Circle of
the Antipedal Triangle of the First Brocard Point. Circumcenter = Center of the Gallatly Circle of
the Antipedal Triangle of the Second Brocard Point. Circumcenter = Midpoint between the Orthocenter
and the de Longchamps Point. Circumcenter = Midpoint between the Steiner
Point and the Tarry Point. Circumcenter = Midpoint between the Bevan Point
and the Incenter. Circumcenter = Reflection of the Orthocenter in the
Nine-Point Center. Circumcenter = Reflection of the Fuhrmann Center
in the Spieker Center. Circumcenter = Reflection of the Symmedian Point
in the Center of the Brocard Circle. Circumcenter = Reflection of the Nine-Point
Center in the Complement of the Nine-Point Center. Circumcenter = Reflection of the Orthocenter of
the Orthic Triangle in the Center of the Taylor Circle. Circumcenter = Product of the Centroid and the
Circumcenter. Circumcenter = Product of the Symmedian Point
and the Symmedian Point of the Anticomplementary Triangle. Circumcenter = Miquel Point of the Centroid. Circumcenter = Inverse of the Incenter in the
Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Centroid in the
Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Orthocenter in the
Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Nine-Point Center
in the Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Symmedian Point in
the Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Gergonne Point in
the Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Inverse of the Nagel Point in the
Outer Soddy Circle of the Lucas Central Triangle. Circumcenter = Internal Center of Similitude of
the Circumcircle and the Second Droz-Farny Circle. Circumcenter = Internal Center of Similitude of
the Bevan Circle and the Hexyl Circle. Circumcenter = Internal Center of Similitude of
the Circumcircle and the First Droz-Farny Circle of the Medial Triangle. Circumcenter = Internal Center of Similitude of
the Second Droz-Farny Circle and the First Droz-Farny Circle of the Medial
Triangle. Circumcenter = External Center of Similitude of
the Circumcircle and the Second Droz-Farny Circle. Circumcenter = External Center of Similitude of
the Cosine Circle and the Radical Circle of the Lucas Circles. Circumcenter = External Center of Similitude of
the Circumcircle and the First Droz-Farny Circle of the Medial Triangle. Circumcenter = External Center of Similitude of
the Nine-Point Circle and the Nine-Point Circle of the Medial Triangle. Circumcenter = External Center of Similitude of
the Spieker Circle and the Inner Johnson-Yff Circle of the Medial Triangle. Circumcenter = External Center of Similitude of
the Spieker Circle and the Outer Johnson-Yff Circle of the Medial Triangle. Circumcenter = External Center of Similitude of
the First Droz-Farny Circle and the Second Droz-Farny Circle of the Medial
Triangle. Circumcenter = External Center of Similitude of
the Second Droz-Farny Circle and the First Droz-Farny Circle of the Medial
Triangle. Circumcenter = Radical Center of the Triad of
the Circumcircles of the Triangulation Triangles of the Circumcenter. Circumcenter = Radical Center of the Triad of
the Second Droz-Farny Circles of the Triangulation Triangles of the
Orthocenter. Circumcenter = Radical Center of the Triad of
the Parry Circles of the Triangulation Triangles of the Tarry Point. Circumcenter = Radical Center of the Triad of
the Stevanovic Circles of the Triangulation Triangles of the Tarry Point. Circumcenter = Radical Center of the Triad of
the Parry Circles of the Triangulation Triangles of the Steiner Point. Circumcenter = Radical Center of the Triad of
the Stevanovic Circles of the Triangulation Triangles of the Steiner Point. Circumcenter = Radical Center of the Triad of
the Parry Circles of the Triangulation Triangles of the Kiepert-Parry Point. Circumcenter = Radical Center of the Triad of
the Stevanovic Circles of the Triangulation Triangles of the Kiepert-Parry
Point. Circumcenter = Radical Center of the Triad of
the Parry Circles of the Triangulation Triangles of the Parry Point. Circumcenter = Radical Center of the Triad of
the Stevanovic Circles of the Triangulation Triangles of the Parry Point. Circumcenter = Radical Center of the Triad of
the Outer Soddy Circles of the Triangulation Triangles of the Center of the
Inner Soddy Circle. Circumcenter = Radical Center of the Triad of
the Circumcircles of the Corner Triangles of the Anticevian Triangle of the
Symmedian Point. Circumcenter = Perspector of the Medial Triangle
and the Tangential Triangle. Circumcenter = Perspector of the Cevian Triangle
of the Circumcenter and the Anticevian Triangle of the Circumcenter. Circumcenter = Perspector of the Cevian Triangle
of the Schiffler Point and the Excentral Triangle. Circumcenter = Perspector of the Medial Triangle
and the Antipedal Triangle of the Circumcenter. Circumcenter = Perspector of the Cevian Triangle
of the Schiffler Point and the Antipedal Triangle of the Incenter. Circumcenter = Perspector of the Medial Triangle
and the Circum-Incentral Triangle. Circumcenter = Perspector of the Cevian Triangle
of the Circumcenter and the Circumcevian Triangle of the Circumcenter. Circumcenter = Perspector of the Medial Triangle
and the Fuhrmann Triangle. Circumcenter = Perspector of the Medial Triangle
and the First Brocard Triangle. Circumcenter = Perspector of the Medial Triangle
and the Neuberg Triangle. Circumcenter = Perspector of the Medial Triangle
and the Reflected Neuberg Triangle. Circumcenter = Homothetic Center of the Medial
Triangle and the Johnson Triangle. Circumcenter = Perspector of the Cevian Triangle
of the Circumcenter and the Lucas Central Triangle. Circumcenter = Perspector of the Cevian Triangle
of the Nine-Point Center and the Reflection Triangle. Circumcenter = Perspector of the Cevian Triangle
of the Schiffler Point and the Hexyl Triangle. Circumcenter = Perspector of the Tangential
Triangle and the Pedal Triangle of the Circumcenter. Circumcenter = Perspector of the Anticevian
Triangle of the Circumcenter and the Circumcevian Triangle of the
Circumcenter. Circumcenter = Perspector of the Tangential
Triangle and the Circum-Incentral Triangle. Circumcenter = Homothetic Center of the
Excentral Triangle and the Hexyl Triangle. Circumcenter = Perspector of the Anticevian
Triangle of the Circumcenter and the Lucas Central Triangle. Circumcenter = Perspector of the Tangential
Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the Tangential
Triangle and the First Brocard Triangle. Circumcenter = Perspector of the Tangential
Triangle and the Neuberg Triangle. Circumcenter = Perspector of the Tangential
Triangle and the Reflected Neuberg Triangle. Circumcenter = Perspector of the Tangential
Triangle and the Johnson Triangle. For any Kiepert Triangle, the Circumcenter is
the Perspector of the Tangential Triangle and the Kiepert Triangle. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the Antipedal Triangle of the Circumcenter. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the Circum-Incentral Triangle. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the Fuhrmann Triangle. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the First Brocard Triangle. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the Neuberg Triangle. Circumcenter = Perspector of the Pedal Triangle
of the Circumcenter and the Reflected Neuberg Triangle. Circumcenter = Homothetic Center of the Pedal
Triangle of the Circumcenter and the Johnson Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the Circum-Incentral Triangle. Circumcenter = Homothetic Center of the
Antipedal Triangle of the Incenter and the Hexyl Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the Fuhrmann Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the First Brocard Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the Neuberg Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the Reflected Neuberg Triangle. Circumcenter = Perspector of the Antipedal
Triangle of the Circumcenter and the Johnson Triangle. For any Kiepert Triangle, the Circumcenter is
the Perspector of the Antipedal Triangle of the Circumcenter and the Kiepert
Triangle. Circumcenter = Perspector of the
Circum-Incentral Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the
Circum-Incentral Triangle and the First Brocard Triangle. Circumcenter = Perspector of the
Circum-Incentral Triangle and the Neuberg Triangle. Circumcenter = Perspector of the
Circum-Incentral Triangle and the Reflected Neuberg Triangle. Circumcenter = Perspector of the
Circum-Incentral Triangle and the Johnson Triangle. Circumcenter = Perspector of the Circumcevian
Triangle of the Circumcenter and the Lucas Central Triangle. Circumcenter = Perspector of the Circumcevian
Triangle of the External Center of Similitude of the Incircle and the
Circumcircle and the Mixtilinear Triangle. Circumcenter = Perspector of the Fuhrmann
Triangle and the First Brocard Triangle. Circumcenter = Perspector of the Fuhrmann
Triangle and the Neuberg Triangle. Circumcenter = Perspector of the Fuhrmann
Triangle and the Reflected Neuberg Triangle. Circumcenter = Perspector of the Fuhrmann
Triangle and the Johnson Triangle. Circumcenter = Perspector of the First Brocard
Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the First Brocard
Triangle and the Neuberg Triangle. Circumcenter = Perspector of the First Brocard
Triangle and the Reflected Neuberg Triangle. Circumcenter = Perspector of the First Brocard
Triangle and the Johnson Triangle. Circumcenter = Perspector of the Neuberg
Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the Neuberg
Triangle and the First Brocard Triangle. Circumcenter = Perspector of the Neuberg
Triangle and the Reflected Neuberg Triangle. Circumcenter = Perspector of the Neuberg
Triangle and the Johnson Triangle. Circumcenter = Perspector of the Reflected
Neuberg Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the Reflected
Neuberg Triangle and the First Brocard Triangle. Circumcenter = Perspector of the Reflected
Neuberg Triangle and the Neuberg Triangle. Circumcenter = Perspector of the Reflected
Neuberg Triangle and the Johnson Triangle. Circumcenter = Perspector of the Johnson
Triangle and the Fuhrmann Triangle. Circumcenter = Perspector of the Johnson
Triangle and the First Brocard Triangle. Circumcenter = Perspector of the Johnson
Triangle and the Neuberg Triangle. Circumcenter = Perspector of the Johnson
Triangle and the Reflected Neuberg Triangle. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the Centroids of the Triangulation Triangles of the de
Longchamps Point. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the Circumcenters of the Corner Triangles of the
Centroid. Circumcenter = Perspector of Triangle ABC and
the Triangle of the Orthocenters of the Corner Triangles of the Orthocenter. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the Orthocenters of the Anticevian Corner Triangles of
the Centroid. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the reflections of the Nine-Point Center in the sides of
the Medial Triangle. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the Circumcenter in the sides of the
Orthic Triangle. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the Orthocenter in the sides of the
Excentral Triangle. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the reflections of the Circumcenter in the sides of the
Tangential Triangle. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the reflections of the Orthocenter in the vertices of the
Medial Triangle. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the Circumcenter in the vertices of the
Cevian Triangle of the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the Circumcenter in the vertices of the
Anticevian Triangle of the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the vertices of the Cevian Triangle of the
Circumcenter in the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the vertices of the Orthic Triangle in the
Center of the Taylor Circle. Circumcenter = Homothetic Center of Triangle ABC
and the Triangle of the reflections of the vertices of the Anticomplementary
Triangle in the Nine-Point Center. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the vertices of the Anticevian Triangle of
the Circumcenter in the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Triangle of the reflections of the vertices of the Anticevian Triangle of
the Nine-Point Center in the Center of the Taylor Circle. Circumcenter = Perspector of Triangle ABC and
the Outer Apollonius Triangle of the Lucas Circles of the Cevian Triangle of
the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Outer Apollonius Triangle of the Lucas Circles of the Anticevian Triangle
of the Circumcenter. Circumcenter = Homothetic Center of Triangle ABC
and the Outer Apollonius Triangle of the Lucas Circles of the Circumcevian
Triangle of the Circumcenter. Circumcenter = Perspector of Triangle ABC and
the Outer Apollonius Triangle of the Lucas Circles of the Lucas Central
Triangle. Circumcenter = Complement of the Orthocenter. Circumcenter = Complement of the Complement of
the de Longchamps Point. Circumcenter = Isogonal Conjugate of the
Complement of the de Longchamps Point. Circumcenter = Anticomplement of the Nine-Point
Center. Circumcenter = Isogonal Conjugate of the
Anticomplement of the Circumcenter. Circumcenter = Isogonal Conjugate of the
Orthocenter. Circumcenter = Complement of the Isogonal
Conjugate of the Circumcenter. Circumcenter = Anticomplement of the Isogonal
Conjugate of the Kosnita Point. Circumcenter = Complement of the Cyclocevian
Conjugate of the Centroid. Circumcenter = Isogonal Conjugate of the
Cyclocevian Conjugate of the Centroid. Circumcenter = Complement of the de Longchamps
Point of the Medial Triangle. Circumcenter = Anticomplement of the
Circumcenter of the Orthic Triangle. Circumcenter = Isogonal Conjugate of the
Anticomplement of the Orthocenter of the Medial Triangle. Circumcenter = Isogonal Conjugate of the de Longchamps
Point of the Medial Triangle. Circumcenter = Complement of the Isogonal
Conjugate of the Orthocenter of the Medial Triangle. The Circumcenter lies on the Brocard Circle. The Circumcenter lies on the Orthocentroidal
Circle of the Medial Triangle. The Circumcenter lies on the Hexyl Circle of the
Orthic Triangle. The Circumcenter lies on the Bevan Circle of the
Tangential Triangle. The Circumcenter lies on the Orthocentroidal
Circle of the Pedal Triangle of the Circumcenter. The Circumcenter lies on the Hexyl Circle of the
Pedal Triangle of the Orthocenter. The Circumcenter lies on the Bevan Circle of the
Antipedal Triangle of the Circumcenter. The Circumcenter lies on the Orthocentroidal
Circle of the Antipedal Triangle of the Symmedian Point. The Circumcenter lies on the Parry Circle of the
Antipedal Triangle of the Symmedian Point. The Circumcenter lies on the Moses Circle of the
Antipedal Triangle of the First Beltrami Point. The Circumcenter lies on the Moses Circle of the
Antipedal Triangle of the Second Beltrami Point. For any Triangle Center, the Circumcenter lies
on the Brocard Circle of the Circumcevian Triangle of the Triangle Center. The Circumcenter lies on the Circumcircle of the
First Brocard Triangle. The Circumcenter lies on the Circumcircle of the
Second Brocard Triangle. The Circumcenter lies on the Outer Soddy Circle
of the Lucas Central Triangle. The Circumcenter lies on the Orthocentroidal
Circle of the Johnson Triangle. The Circumcenter lies on the Circumcircle of the
Inner Gallatly-Kiepert Triangle. The Circumcenter lies on the Outer Apollonius
Circle of the Mixtilinear Incircles of the Second Brocard Triangle. The Circumcenter lies on the Outer Apollonius
Circle of the Lucas Circles of the First Brocard Triangle. The Circumcenter lies on the Outer Apollonius
Circle of the Lucas Circles of the Second Brocard Triangle. The Circumcenter lies on the Outer Apollonius
Circle of the Lucas Circles of the Inner Gallatly-Kiepert Triangle. The Circumcenter lies on the Line through the
Incenter and the Weill Point. The Circumcenter lies on the Line through the
Incenter and the Moses Point. The Circumcenter lies on the Line through the
Incenter and the Internal Center of Similitude of the Incircle and the
Circumcircle. The Circumcenter lies on the Line through the
Centroid and the Orthocenter. The Circumcenter lies on the Line through the
Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Centroid and the de Longchamps Point. The Circumcenter lies on the Line through the
Centroid and the Exeter Point. The Circumcenter lies on the Line through the
Centroid and the Schiffler Point. The Circumcenter lies on the Line through the
Centroid and the Gibert Point. The Circumcenter lies on the Line through the
Centroid and the Skordev Point. The Circumcenter lies on the Line through the
Orthocenter and the de Longchamps Point. The Circumcenter lies on the Line through the
Orthocenter and the Schiffler Point. The Circumcenter lies on the Line through the
Orthocenter and the Skordev Point. The Circumcenter lies on the Line through the
Symmedian Point and the Third Power Point. The Circumcenter lies on the Line through the
Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Nine-Point Center and the de Longchamps Point. The Circumcenter lies on the Line through the
Nine-Point Center and the Schiffler Point. The Circumcenter lies on the Line through the
Nine-Point Center and the Skordev Point. The Circumcenter lies on the Line through the
Outer Fermat Point and the Outer Napoleon Point. The Circumcenter lies on the Line through the
Inner Fermat Point and the Inner Napoleon Point. The Circumcenter lies on the Line through the
First Isodynamic Point and the Symmedian Point. The Circumcenter lies on the Line through the
First Isodynamic Point and the Second Isodynamic Point. The Circumcenter lies on the Line through the
First Isodynamic Point and the Third Power Point. The Circumcenter lies on the Line through the First
Isodynamic Point and the Inner Kenmotu Point. The Circumcenter lies on the Line through the
First Isodynamic Point and the Outer Kenmotu Point. The Circumcenter lies on the Line through the
Second Isodynamic Point and the Symmedian Point. The Circumcenter lies on the Line through the
Second Isodynamic Point and the Third Power Point. The Circumcenter lies on the Line through the
Exeter Point and the Orthocenter. The Circumcenter lies on the Line through the
Exeter Point and the Nine-Point Center. The Circumcenter lies on the Line through the
Exeter Point and the de Longchamps Point. The Circumcenter lies on the Line through the
Exeter Point and the Schiffler Point. The Circumcenter lies on the Line through the
Exeter Point and the Gibert Point. The Circumcenter lies on the Line through the
Exeter Point and the Skordev Point. The Circumcenter lies on the Line through the
Schiffler Point and the de Longchamps Point. The Circumcenter lies on the Line through the
Schiffler Point and the Skordev Point. The Circumcenter lies on the Line through the
Gibert Point and the Orthocenter. The Circumcenter lies on the Line through the
Gibert Point and the Nine-Point Center. The Circumcenter lies on the Line through the
Gibert Point and the de Longchamps Point. The Circumcenter lies on the Line through the
Gibert Point and the Schiffler Point. The Circumcenter lies on the Line through the
Gibert Point and the Skordev Point. The Circumcenter lies on the Line through the
Moses Point and the Weill Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the Symmedian Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the First Isodynamic Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the Second Isodynamic Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the Third Power Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the Inner Kenmotu Point. The Circumcenter lies on the Line through the Brocard
Midpoint and the Outer Kenmotu Point. The Circumcenter lies on the Line through the
Brocard Midpoint and the Danneels-Apollonius Prespector. The Circumcenter lies on the Line through the
Steiner Point and the Tarry Point. The Circumcenter lies on the Line through the
Fuhrmann Center and the Spieker Center. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Symmedian Point. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Second Isodynamic Point. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Third Power Point. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Outer Kenmotu Point. The Circumcenter lies on the Line through the
Outer Kenmotu Point and the Symmedian Point. The Circumcenter lies on the Line through the
Outer Kenmotu Point and the Second Isodynamic Point. The Circumcenter lies on the Line through the
Outer Kenmotu Point and the Third Power Point. The Circumcenter lies on the Line through the
Evans Perspector and the Incenter. The Circumcenter lies on the Line through the
Evans Perspector and the Weill Point. The Circumcenter lies on the Line through the
Evans Perspector and the Moses Point. The Circumcenter lies on the Line through the
Evans Perspector and the Internal Center of Similitude of the Incircle and
the Circumcircle. The Circumcenter lies on the Line through the
Evans Perspector and the External Center of Similitude of the Incircle and
the Circumcircle. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Symmedian Point. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the First Isodynamic Point. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Second Isodynamic Point. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Third Power Point. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Inner Kenmotu Point. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Outer Kenmotu Point. The Circumcenter lies on the Line through the
Skordev Point and the de Longchamps Point. The Circumcenter lies on the Line through the
First Beltrami Point and the First Brocard Point. The Circumcenter lies on the Line through the
Second Beltrami Point and the Second Brocard Point. The Circumcenter lies on the Line through the
Incenter and the Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
Incenter and the Inverse of the Incenter in the Circumcircle. The Circumcenter lies on the Line through the
Incenter and the Isogonal Conjugate of the Mittenpunkt. The Circumcenter lies on the Line through the
Centroid and the Circumcenter of the Tangential Triangle. The Circumcenter lies on the Line through the
Centroid and the Far-Out Point. The Circumcenter lies on the Line through the
Centroid and the Inverse of the Orthocenter in the Circumcircle. The Circumcenter lies on the Line through the
Centroid and the Complement of the Nine-Point Center. The Circumcenter lies on the Line through the
Gergonne Point and the Inverse of the Gergonne Point in the Circumcircle. The Circumcenter lies on the Line through the
Mittenpunkt and the Orthocenter of the Extouch Triangle. The Circumcenter lies on the Line through the
First Isodynamic Point and the Orthocenter of the Incentral Triangle. The Circumcenter lies on the Line through the
First Isodynamic Point and the Orthocenter of the Orthic Triangle. The Circumcenter lies on the Line through the
First Isodynamic Point and the Schoute Center. The Circumcenter lies on the Line through the
First Isodynamic Point and the Isogonal Conjugate of the Spieker Center. The Circumcenter lies on the Line through the
Exeter Point and the Far-Out Point. The Circumcenter lies on the Line through the
Exeter Point and the Inverse of the Orthocenter in the Circumcircle. The Circumcenter lies on the Line through the
Gibert Point and the Inverse of the Orthocenter in the Circumcircle. The Circumcenter lies on the Line through the
Moses Point and the Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Orthocenter of the Incentral Triangle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Orthocenter of the Orthic Triangle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Center of the Apollonius Circle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Center of the Brocard Circle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Center of the Inner Lucas Circle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Center of the Taylor Circle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Schoute Center. The Circumcenter lies on the Line through the
Brocard Midpoint and the Isogonal Conjugate of the Spieker Center. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Incircle and the Circumcircle and the
Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Incircle and the Circumcircle and the
Inverse of the Incenter in the Circumcircle. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Incircle and the Circumcircle and the
Isogonal Conjugate of the Mittenpunkt. The Circumcenter lies on the Line through the
External Center of Similitude of the Incircle and the Circumcircle and the
Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
External Center of Similitude of the Incircle and the Circumcircle and the
Inverse of the Incenter in the Circumcircle. The Circumcenter lies on the Line through the
External Center of Similitude of the Incircle and the Circumcircle and the
Isogonal Conjugate of the Mittenpunkt. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Orthocenter of the Incentral Triangle. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Orthocenter of the Orthic Triangle. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Schoute Center. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Isogonal Conjugate of the Spieker Center. The Circumcenter lies on the Line through the
Outer Kenmotu Point and the Schoute Center. The Circumcenter lies on the Line through the
Evans Perspector and the Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
Evans Perspector and the Inverse of the Incenter in the Circumcircle. The Circumcenter lies on the Line through the
Evans Perspector and the Isogonal Conjugate of the Mittenpunkt. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Orthocenter of the Incentral Triangle.
The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Orthocenter of the Orthic Triangle. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Schoute Center. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Isogonal Conjugate of the Spieker
Center. The Circumcenter lies on the Line through the
Incenter and the Perspector of the Orthic Triangle and the Excentral
Triangle. The Circumcenter lies on the Line through the
Incenter and the Internal Center of Similitude of the Bevan Circle and the
Incircle. The Circumcenter lies on the Line through the
Centroid and the Homothetic Center of the Orthic Triangle and the Tangential
Triangle. The Circumcenter lies on the Line through the
Centroid and the Midpoint of the Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Centroid and the Midpoint of the Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
First Isodynamic Point and the Internal Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Exeter Point and the Homothetic Center of the Orthic Triangle and the
Tangential Triangle. The Circumcenter lies on the Line through the
Exeter Point and the Midpoint of the Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Exeter Point and the Midpoint of the Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Gibert Point and the Homothetic Center of the Orthic Triangle and the
Tangential Triangle. The Circumcenter lies on the Line through the
Gibert Point and the Midpoint of the Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Gibert Point and the Midpoint of the Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Moses Point and the Perspector of the Orthic Triangle and the Excentral
Triangle. The Circumcenter lies on the Line through the
Brocard Midpoint and the Internal Center of Similitude of the Apollonius
Circle and the Circumcircle. The Circumcenter lies on the Line through the
Brocard Midpoint and the External Center of Similitude of the Apollonius
Circle and the Circumcircle. The Circumcenter lies on the Line through the
Fuhrmann Center and the Perspector of the Extouch Triangle and the Tangential
Triangle. The Circumcenter lies on the Line through the
Fuhrmann Center and the Midpoint of the Circumcenter and the Spieker Center. The Circumcenter lies on the Line through the
Fuhrmann Center and the Internal Center of Similitude of the Circumcircle and
the Spieker Circle. The Circumcenter lies on the Line through the
Inner Kenmotu Point and the Internal Center of Similitude of the Apollonius
Circle and the Circumcircle. The Circumcenter lies on the Line through the
Evans Perspector and the Perspector of the Orthic Triangle and the Excentral
Triangle. The Circumcenter lies on the Line through the
Evans Perspector and the Midpoint of the Circumcenter and the Incenter. The Circumcenter lies on the Line through the
Evans Perspector and the Internal Center of Similitude of the Bevan Circle
and the Incircle. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the Internal Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Danneels-Apollonius Prespector and the External Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Orthocenter of the Incentral Triangle and the Orthocenter of the Orthic
Triangle. The Circumcenter lies on the Line through the
Orthocenter of the Incentral Triangle and the Schoute Center. The Circumcenter lies on the Line through the
Symmedian Point of the Medial Triangle and the Symmedian Point of the
Tangential Triangle. The Circumcenter lies on the Line through the
Orthocenter of the Orthic Triangle and the Schoute Center. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Orthocenter of the Intouch
Triangle. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Inverse of the Incenter in the
Circumcircle. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Isogonal Conjugate of the
Mittenpunkt. The Circumcenter lies on the Line through the
Bevan Point and the Orthocenter of the Intouch Triangle. The Circumcenter lies on the Line through the
Bevan Point and the Centroid of the Excentral Triangle. The Circumcenter lies on the Line through the
Bevan Point and the Inverse of the Incenter in the Circumcircle. The Circumcenter lies on the Line through the
Bevan Point and the Isogonal Conjugate of the Mittenpunkt. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Far-Out Point. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Inverse of the Orthocenter in
the Circumcircle. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Complement of the Nine-Point
Center. The Circumcenter lies on the Line through the
Inverse of the Incenter in the Circumcircle and the Orthocenter of the
Intouch Triangle. The Circumcenter lies on the Line through the
Inverse of the Incenter in the Circumcircle and the Isogonal Conjugate of the
Mittenpunkt. The Circumcenter lies on the Line through the
Far-Out Point and the Inverse of the Orthocenter in the Circumcircle. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Far-Out Point. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Inverse of the Orthocenter in the
Circumcircle. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Complement of the Spieker Center. The Circumcenter lies on the Line through the
Isogonal Conjugate of the Mittenpunkt and the Orthocenter of the Intouch
Triangle. The Circumcenter lies on the Line through the
Isogonal Conjugate of the Spieker Center and the Orthocenter of the Incentral
Triangle. The Circumcenter lies on the Line through the
Isogonal Conjugate of the Spieker Center and the Orthocenter of the Orthic
Triangle. The Circumcenter lies on the Line through the
Isogonal Conjugate of the Spieker Center and the Schoute Center. The Circumcenter lies on the Line through the
Isotomic Conjugate of the Circumcenter and the Isotomic Conjugate of the
Nine-Point Center. The Circumcenter lies on the Line through the
Incenter of the Orthic Triangle and the Perspector of Triangle ABC and the
Intouch Triangle of the Orthic Triangle. The Circumcenter lies on the Line through the
Orthocenter of the Intouch Triangle and the Perspector of the Orthic Triangle
and the Excentral Triangle. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Perspector of the Orthic Triangle
and the Excentral Triangle. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Midpoint of the Circumcenter and
the Incenter. The Circumcenter lies on the Line through the
Centroid of the Excentral Triangle and the Internal Center of Similitude of
the Bevan Circle and the Incircle. The Circumcenter lies on the Line through the
Bevan Point and the Perspector of the Orthic Triangle and the Excentral
Triangle. The Circumcenter lies on the Line through the
Bevan Point and the Midpoint of the Circumcenter and the Incenter. The Circumcenter lies on the Line through the
Bevan Point and the Internal Center of Similitude of the Bevan Circle and the
Incircle. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Homothetic Center of the
Orthic Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Midpoint of the Centroid and
the Circumcenter. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Midpoint of the Centroid and
the Nine-Point Center. The Circumcenter lies on the Line through the
Circumcenter of the Tangential Triangle and the Midpoint of the Nine-Point
Center and the Orthocenter. The Circumcenter lies on the Line through the
Center of the Orthocentroidal Circle and the Homothetic Center of the Orthic
Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Center of the Orthocentroidal Circle and the Midpoint of the Centroid and the
Nine-Point Center. The Circumcenter lies on the Line through the
Center of the Orthocentroidal Circle and the Midpoint of the Nine-Point
Center and the Orthocenter. The Circumcenter lies on the Line through the
Center of the Inner Lucas Circle and the Internal Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Center of the Inner Lucas Circle and the External Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Center of the Taylor Circle and the Internal Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Center of the Taylor Circle and the External Center of Similitude of the
Apollonius Circle and the Circumcircle. The Circumcenter lies on the Line through the
Inverse of the Incenter in the Circumcircle and the Perspector of the Orthic
Triangle and the Excentral Triangle. The Circumcenter lies on the Line through the
Inverse of the Incenter in the Circumcircle and the Midpoint of the
Circumcenter and the Incenter. The Circumcenter lies on the Line through the
Far-Out Point and the Homothetic Center of the Orthic Triangle and the
Tangential Triangle. The Circumcenter lies on the Line through the
Far-Out Point and the Midpoint of the Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Far-Out Point and the Midpoint of the Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Inverse of the Orthocenter in the Circumcircle and the Midpoint of the
Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Inverse of the Orthocenter in the Circumcircle and the Midpoint of the
Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Inverse of the Gergonne Point in the Circumcircle and the Midpoint of the
Circumcenter and the Gergonne Point. The Circumcenter lies on the Line through the
Inverse of the Nagel Point in the Circumcircle and the Midpoint of the
Circumcenter and the Nagel Point. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Homothetic Center of the Orthic
Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Midpoint of the Centroid and the
Circumcenter. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Midpoint of the Centroid and the
Nine-Point Center. The Circumcenter lies on the Line through the
Complement of the Nine-Point Center and the Midpoint of the Nine-Point Center
and the Orthocenter. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Perspector of the Intouch Triangle and
the Tangential Triangle. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Midpoint of the Incenter and the
Orthocenter. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Midpoint of the Incenter and the
Mittenpunkt. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Midpoint of the Gergonne Point and the
Orthocenter. The Circumcenter lies on the Line through the
Complement of the Mittenpunkt and the Midpoint of the Gergonne Point and the
Spieker Center. The Circumcenter lies on the Line through the
Complement of the Spieker Center and the Perspector of the Intouch Triangle
and the Tangential Triangle. The Circumcenter lies on the Line through the
Complement of the Spieker Center and the Midpoint of the Incenter and the
Orthocenter. The Circumcenter lies on the Line through the
Complement of the Spieker Center and the Midpoint of the Incenter and the
Mittenpunkt. The Circumcenter lies on the Line through the
Complement of the Spieker Center and the Midpoint of the Gergonne Point and
the Orthocenter. The Circumcenter lies on the Line through the
Complement of the Spieker Center and the Midpoint of the Gergonne Point and
the Spieker Center. The Circumcenter lies on the Line through the
Isogonal Conjugate of the Mittenpunkt and the Perspector of the Orthic
Triangle and the Excentral Triangle. The Circumcenter lies on the Line through the
Homothetic Center of the Orthic Triangle and the Tangential Triangle and the
Midpoint of the Centroid and the Circumcenter. The Circumcenter lies on the Line through the
Homothetic Center of the Orthic Triangle and the Tangential Triangle and the
Midpoint of the Centroid and the Nine-Point Center. The Circumcenter lies on the Line through the
Homothetic Center of the Orthic Triangle and the Tangential Triangle and the
Midpoint of the Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Midpoint of the Incenter and the Orthocenter and the Perspector of the
Intouch Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Midpoint of the Incenter and the Mittenpunkt and the Perspector of the
Intouch Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Midpoint of the Incenter and the Mittenpunkt and the Midpoint of the Incenter
and the Orthocenter. The Circumcenter lies on the Line through the
Midpoint of the Centroid and the Nine-Point Center and the Midpoint of the
Nine-Point Center and the Orthocenter. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Orthocenter and the Perspector of the
Intouch Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Orthocenter and the Midpoint of the
Incenter and the Orthocenter. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Orthocenter and the Midpoint of the
Incenter and the Mittenpunkt. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Orthocenter and the Midpoint of the
Gergonne Point and the Spieker Center. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Spieker Center and the Perspector of
the Intouch Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
Midpoint of the Gergonne Point and the Spieker Center and the Midpoint of the
Incenter and the Orthocenter. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Bevan Circle and the Incircle and the
Perspector of the Orthic Triangle and the Excentral Triangle. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Bevan Circle and the Incircle and the
Midpoint of the Circumcenter and the Incenter. The Circumcenter lies on the Line through the
Internal Center of Similitude of the Bevan Circle and the Nine-Point Circle
and the Midpoint of the Nine-Point Center and the Spieker Center. The Circumcenter lies on the Line through the
External Center of Similitude of the Circumcircle and the Spieker Circle and
the Perspector of the Extouch Triangle and the Tangential Triangle. The Circumcenter lies on the Line through the
External Center of Similitude of the Circumcircle and the Spieker Circle and
the Midpoint of the Circumcenter and the Spieker Center. The Circumcenter lies on the Line through the
External Center of Similitude of the Circumcircle and the Spieker Circle and
the Internal Center of Similitude of the Circumcircle and the Spieker Circle.
The Circumcenter lies on the Line through the
External Center of Similitude of the Apollonius Circle and the Circumcircle
and the Internal Center of Similitude of the Apollonius Circle and the
Circumcircle. Invitation
The reader is
invited to submit a note/paper containing
Definitions and Conventions
We use the
definitions and conventions in accordance with [1 - 6] and papers published
in this journal. The LevelThe Machine for Questions and Answers is used to produce results
in this paper. Currently the Machine has 6 levels of depths - 0,1,2,3,4,5. We
use for this paper the level 0, that is, the Machine produces only elementary
results. If we need deeper investigation, we have to use a level bigger than
0. Since the Machine for Questions and Answers produces too many results, it
is suitable we to use bigger levels upon request, that is, for specific
questions. References
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