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Journal of Computer-Generated Euclidean Geometry |
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Nine-Point Center Deko Dekov
Nine-Point Center = Circumcenter of the Orthic Triangle. Nine-Point Center = Circumcenter of the Pedal
Triangle of the Circumcenter. Nine-Point Center = Circumcenter of the Pedal
Triangle of the Orthocenter. Nine-Point Center = Circumcenter of the Euler
Triangle. Nine-Point Center = Circumcenter of the
Feuerbach Triangle. Nine-Point Center = Nine-Point Center of the
Fuhrmann Triangle. Nine-Point Center = Nine-Point Center of the
Johnson Triangle. Nine-Point Center = Center of the Nine-Point
Circle. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Medial Triangle. Nine-Point Center = Center of the Circumcircle
of the Orthic Triangle. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Orthic Triangle. Nine-Point Center = Center of the Circumcircle
of the Pedal Triangle of the Circumcenter. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Pedal Triangle of the Circumcenter. Nine-Point Center = Center of the Circumcircle
of the Pedal Triangle of the Orthocenter. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Pedal Triangle of the Orthocenter. Nine-Point Center = Center of the Circumcircle
of the Euler Triangle. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Euler Triangle. Nine-Point Center = Center of the Circumcircle
of the Feuerbach Triangle. Nine-Point Center = Center of the Second
Droz-Farny Circle of the Feuerbach Triangle. Nine-Point Center = Center of the Nine-Point
Circle of the Fuhrmann Triangle. Nine-Point Center = Center of the Nine-Point
Circle of the Johnson Triangle. Nine-Point Center = Center of the Inner
Apollonius Circle of the Excircles. Nine-Point Center = Center of the Inner
Apollonius Circle of the Excircles of the Fuhrmann Triangle. Nine-Point Center = Center of the Inner
Apollonius Circle of the Excircles of the Johnson Triangle. Nine-Point Center = Center of the Outer
Apollonius Circle of the Mixtilinear Incircles of the Orthic Triangle. Nine-Point Center = Center of the Outer
Apollonius Circle of the Mixtilinear Incircles of the Pedal Triangle of the
Orthocenter. Nine-Point Center = Center of the Outer
Apollonius Circle of the Mixtilinear Incircles of the Feuerbach Triangle. Nine-Point Center = Center of the Inner
Apollonius Circle of the Triad of the Incircles of the Triangulation
Triangles of the Orthocenter. Nine-Point Center = Center of the Inner
Apollonius Circle of the Triad of the Moses Circles of the Triangulation
Triangles of the Orthocenter. Nine-Point Center = Midpoint between the
Circumcenter and the Orthocenter. Nine-Point Center = Midpoint between the
Fuhrmann Center and the Incenter. Nine-Point Center = Midpoint between the
Orthocenter of the Tangential Triangle and the Prasolov Point. Nine-Point Center = Midpoint between the Center
of the Orthocentroidal Circle and the Centroid. Nine-Point Center = Midpoint between the
Midpoint of the Incenter and the Orthocenter and the Spieker Center. Nine-Point Center = Midpoint between the
Midpoint of the Gergonne Point and the Orthocenter and the Mittenpunkt. Nine-Point Center = Midpoint between the
Midpoint of the Orthocenter and the Symmedian Point and the Symmedian Point
of the Medial Triangle. Nine-Point Center = Midpoint between the
Midpoint of the Orthocenter and the Spieker Center and the Complement of the
Spieker Center. Nine-Point Center = Midpoint between the
Midpoint of the Mittenpunkt and the Orthocenter and the Complement of the
Mittenpunkt. Nine-Point Center = Reflection of the
Circumcenter in the Complement of the Nine-Point Center. Nine-Point Center = Product of the Centroid and
the Nine-Point Center. Nine-Point Center = Product of the Centroid of
the Orthic Triangle and the Isotomic Conjugate of the Symmedian Point. Nine-Point Center = Product of the Symmedian
Point of the Anticomplementary Triangle and the Symmedian Point of the Orthic
Triangle. Nine-Point Center = Inverse of the Circumcenter
in the Orthocentroidal Circle. Nine-Point Center = Inverse of the Circumcenter
in the Circumcircle of the Fourth Brocard Triangle. Nine-Point Center = Inverse of the Orthocenter
in the Orthocentroidal Circle of the Johnson Triangle. Nine-Point Center = Internal Center of
Similitude of the First Droz-Farny Circle and the Second Droz-Farny Circle. Nine-Point Center = Radical Center of the Triad
of the Nine-Point Circles of the Corner Triangles of the Anticevian Triangle
of the Centroid. Nine-Point Center = Perspector of the Cevian
Triangle of the Nine-Point Center and the Circumcevian Triangle of the
Nine-Point Center. Nine-Point Center = Homothetic Center of the
Medial Triangle and the Euler Triangle. Nine-Point Center = Perspector of the Cevian
Triangle of the Nine-Point Center and the Johnson Triangle. Nine-Point Center = Perspector of the Anticevian
Triangle of the Nine-Point Center and the Circumcevian Triangle of the
Nine-Point Center. Nine-Point Center = Perspector of the Excentral
Triangle and the Feuerbach Triangle. Nine-Point Center = Perspector of the Anticevian
Triangle of the Nine-Point Center and the Johnson Triangle. Nine-Point Center = Homothetic Center of the
Pedal Triangle of the Circumcenter and the Euler Triangle. Nine-Point Center = Perspector of the Antipedal
Triangle of the Incenter and the Feuerbach Triangle. Nine-Point Center = Perspector of the
Circumcevian Triangle of the Nine-Point Center and the Johnson Triangle. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Centroids of the Triangulation Triangles
of the Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Circumcenters of the Triangulation
Triangles of the Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the de Longchamps Points of the
Triangulation Triangles of the Orthocenter. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the Schiffler Points of the Triangulation Triangles of
the Orthocenter. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the Exeter Points of the Triangulation Triangles of the
Orthocenter. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the Far-Out Points of the Triangulation Triangles of the
Orthocenter. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the Gibert Points of the Triangulation Triangles of the
Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Centers of the Orthocentroidal Circles
of the Triangulation Triangles of the Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Skordev Points of the Triangulation
Triangles of the Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Nine-Point Centers of the Corner
Triangles of the Centroid. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the Kosnita Points of the Corner Triangles of the
Orthocenter. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Circumcenters of the Anticevian Corner
Triangles of the Centroid. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the Orthocenters of the Anticevian Corner
Triangles of the Symmedian Point. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the reflections of the Kosnita Point in the sides of the
Excentral Triangle. Nine-Point Center = Homothetic Center of
Triangle ABC and the Triangle of the reflections of the Circumcenter in the
vertices of the Medial Triangle. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the reflections of the Nine-Point Center in the vertices
of the Cevian Triangle of the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the reflections of the Nine-Point Center in the vertices
of the Anticevian Triangle of the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the reflections of the vertices of the Cevian Triangle of
the Nine-Point Center in the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Triangle of the reflections of the vertices of the Anticevian
Triangle of the Nine-Point Center in the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Outer Apollonius Triangle of the Lucas Circles of the Cevian Triangle
of the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Outer Apollonius Triangle of the Lucas Circles of the Anticevian
Triangle of the Nine-Point Center. Nine-Point Center = Perspector of Triangle ABC
and the Outer Apollonius Triangle of the Lucas Circles of the Circumcevian
Triangle of the Nine-Point Center. Nine-Point Center = Homothetic Center of
Triangle ABC and the Outer Apollonius Triangle of the Lucas Circles of the
Johnson Triangle. Nine-Point Center = Complement of the
Circumcenter. Nine-Point Center = Complement of the Complement
of the Orthocenter. Nine-Point Center = Isogonal Conjugate of the
Kosnita Point. Nine-Point Center = Complement of the Isogonal
Conjugate of the Orthocenter. Nine-Point Center = Complement of the
Orthocenter of the Medial Triangle. Nine-Point Center = Anticomplement of the
Nine-Point Center of the Medial Triangle. Nine-Point Center = Isogonal Conjugate of the
Anticomplement of the Kosnita Point of the Medial Triangle. Nine-Point Center = Complement of the Isogonal
Conjugate of the de Longchamps Point of the Medial Triangle. Nine-Point Center = Isotomic Conjugate of the
Isogonal Conjugate of the Centroid of the Orthic Triangle. The Nine-Point Center lies on the Brocard Circle
of the Medial Triangle. The Nine-Point Center lies on the Brocard Circle
of the Orthic Triangle. The Nine-Point Center lies on the Brocard Circle
of the Pedal Triangle of the Circumcenter. The Nine-Point Center lies on the Brocard Circle
of the Pedal Triangle of the Orthocenter. The Nine-Point Center lies on the Brocard Circle
of the Euler Triangle. The Nine-Point Center lies on the Brocard Circle
of the Feuerbach Triangle. The Nine-Point Center lies on the Nine-Point
Circle of the First Brocard Triangle. The Nine-Point Center lies on the Nine-Point
Circle of the Inner Gallatly-Kiepert Triangle. The Nine-Point Center lies on the Inner
Apollonius Circle of the Excircles of the First Brocard Triangle. The Nine-Point Center lies on the Inner Apollonius
Circle of the Excircles of the Inner Gallatly-Kiepert Triangle. The Nine-Point Center lies on the Line through
the Incenter and the Second Feuerbach Point. The Nine-Point Center lies on the Line through
the Incenter and the Johnson Midpoint. The Nine-Point Center lies on the Line through
the Centroid and the Circumcenter. The Nine-Point Center lies on the Line through
the Centroid and the Orthocenter. The Nine-Point Center lies on the Line through
the Centroid and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Centroid and the Exeter Point. The Nine-Point Center lies on the Line through
the Centroid and the Schiffler Point. The Nine-Point Center lies on the Line through
the Centroid and the Gibert Point. The Nine-Point Center lies on the Line through
the Centroid and the Skordev Point. The Nine-Point Center lies on the Line through
the Circumcenter and the Orthocenter. The Nine-Point Center lies on the Line through
the Circumcenter and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Circumcenter and the Exeter Point. The Nine-Point Center lies on the Line through
the Circumcenter and the Schiffler Point. The Nine-Point Center lies on the Line through
the Circumcenter and the Gibert Point. The Nine-Point Center lies on the Line through
the Circumcenter and the Skordev Point. The Nine-Point Center lies on the Line through
the Orthocenter and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Orthocenter and the Schiffler Point. The Nine-Point Center lies on the Line through
the Orthocenter and the Skordev Point. The Nine-Point Center lies on the Line through
the First Feuerbach Point and the Incenter. The Nine-Point Center lies on the Line through
the First Feuerbach Point and the Second Feuerbach Point. The Nine-Point Center lies on the Line through
the First Feuerbach Point and the Fuhrmann Center. The Nine-Point Center lies on the Line through
the First Feuerbach Point and the Johnson Midpoint. The Nine-Point Center lies on the Line through
the Inner Fermat Point and the Outer Napoleon Point. The Nine-Point Center lies on the Line through
the Inner Napoleon Point and the Outer Fermat Point. The Nine-Point Center lies on the Line through
the Exeter Point and the Orthocenter. The Nine-Point Center lies on the Line through
the Exeter Point and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Exeter Point and the Schiffler Point. The Nine-Point Center lies on the Line through
the Exeter Point and the Gibert Point. The Nine-Point Center lies on the Line through
the Exeter Point and the Skordev Point. The Nine-Point Center lies on the Line through
the Schiffler Point and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Schiffler Point and the Skordev Point. The Nine-Point Center lies on the Line through
the Gibert Point and the Orthocenter. The Nine-Point Center lies on the Line through
the Gibert Point and the de Longchamps Point. The Nine-Point Center lies on the Line through
the Gibert Point and the Schiffler Point. The Nine-Point Center lies on the Line through
the Gibert Point and the Skordev Point. The Nine-Point Center lies on the Line through
the Brocard Midpoint and the Kiepert Center. The Nine-Point Center lies on the Line through
the Prasolov Point and the Symmedian Point. The Nine-Point Center lies on the Line through
the Kiepert-Parry Point and the Kosnita Point. The Nine-Point Center lies on the Line through
the Fuhrmann Center and the Incenter. The Nine-Point Center lies on the Line through
the Fuhrmann Center and the Second Feuerbach Point. The Nine-Point Center lies on the Line through
the Fuhrmann Center and the Johnson Midpoint. The Nine-Point Center lies on the Line through
the Outer Vecten Point and the Symmedian Point. The Nine-Point Center lies on the Line through
the Outer Vecten Point and the Prasolov Point. The Nine-Point Center lies on the Line through
the Inner Vecten Point and the Symmedian Point. The Nine-Point Center lies on the Line through
the Inner Vecten Point and the Prasolov Point. The Nine-Point Center lies on the Line through
the Inner Vecten Point and the Outer Vecten Point. The Nine-Point Center lies on the Line through
the Johnson Midpoint and the Second Feuerbach Point. The Nine-Point Center lies on the Line through
the Skordev Point and the de Longchamps Point. 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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