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Journal of Computer-Generated Euclidean Geometry |
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Inner Johnson Triangles Deko Dekov
Given three circles (A),(B) and (C) with noncollinear
centers A,B and C, respectively. Let A1 be the Internal Similitude
Center of (B) and (C). Similarly define B1 and C1. The
triangle A1B1C1 is called the Inner
Johnson Triangle of circles (A), (B), (C). See the Figure:
(A), (B), (C) - circles; It is well known (see e.g. the Weisstein's
encyclopedia [5]) that triangle ABC and the Inner Johnson Triangle of circles
(A), (B), (C) are perspective. See the Figure:
(A), (B), (C) - circles; Result 816 from the Quim Castellsaguer, The
Triangles Web [1]: Triangle ABC and the Inner Johnson Triangle of
the Lucas Circles are perspective with perspector the Inner Kenmotu Point. See the Figure:
(A1), (B1), (C1)
- Lucas Circles; The Inner Johnson Triangle of the Excircles
coincides with triangle ABC. See the Figure:
(A1), (B1), (C1)
- Excircles. Examples
The Machine for
Questions and Answers gives perspectives between triangles. Examples of
perspectives between triangles and Inner Johnson triangles are given below.
In the examples below the perspectors are between the basic points. Triangle ABC and the Inner Johnson Triangle of
the Mixtilinear Incircles are perspective with perspector the Internal Center
of Similitude of the Bevan Circle and the Incircle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles are perspective with perspector the Gergonne Point. Triangle ABC and the Inner Johnson Triangle of
the Malfatti Circles are perspective with perspector the First Ajima-Malfatti
Point. Triangle ABC and the Inner Johnson Triangle of
the Lucas Circles are perspective with perspector the Inner Kenmotu Point. Triangle ABC and the Inner Johnson Triangle of
the Neuberg Circles are perspective with perspector the Incenter. See the Figure:
(A1), (B1), (C1)
- Neuberg Circles; Triangle ABC and the Inner Johnson Triangle of
the Reflected Neuberg Circles are perspective with perspector the Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Pedal Triangle of the Incenter are perspective with
perspector the Gergonne Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Pedal Triangle of the Circumcenter are homothetic with
homothetic center the Centroid. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Pedal Triangle of the Orthocenter are perspective with
perspector the Orthocenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Pedal Triangle of the de Longchamps Point are
perspective with perspector the Symmedian Point of the Anticomplementary
Triangle. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Pedal Triangle of the Bevan Point are perspective with
perspector the Nagel Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Antipedal Triangle of the Incenter are perspective with
perspector the Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Antipedal Triangle of the Circumcenter are perspective
with perspector the Symmedian Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Antipedal Triangle of the Orthocenter are homothetic
with homothetic center the Centroid. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Antipedal Triangle of the de Longchamps Point are
perspective with perspector the Orthocenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Antipedal Triangle of the Bevan Point are perspective
with perspector the Isogonal Conjugate of the Mittenpunkt. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Euler Triangle are homothetic with homothetic center the
Orthocenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Feuerbach Triangle are perspective with perspector the
Second Feuerbach Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Extangents Triangle are perspective with perspector the
Orthocenter of the Intouch Triangle. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Mixtilinear Triangle are perspective with perspector the
Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Mid-Arc Triangle are perspective with perspector the
Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Triangle of the reflections are perspective with
perspector the Orthocenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the First Brocard Triangle are perspective with perspector
the Isotomic Conjugate of the Symmedian Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Second Brocard Triangle are perspective with perspector
the Symmedian Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Third Brocard Triangle are perspective with perspector
the Third Power Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Fourth Brocard Triangle are perspective with perspector
the Centroid. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Yff Central Triangle are perspective with perspector the
Incenter of the Intouch Triangle. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Lucas Central Triangle are perspective with perspector
the Circumcenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Neuberg Triangle are perspective with perspector the
Tarry Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Johnson Triangle are homothetic with homothetic center
the Nine-Point Center. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Inner Johnson-Yff Triangle are homothetic with
homothetic center the Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Outer Johnson-Yff Triangle are homothetic with
homothetic center the Incenter. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Apollonius Triangle are perspective with perspector the
Apollonius Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Inner Gallatly-Kiepert Triangle are perspective with
perspector the Isotomic Conjugate of the Symmedian Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the Inner Lemoine-Kiepert Triangle are perspective with
perspector the Tarry Point. Triangle ABC and the Inner Johnson Triangle of
the Excircles of the First Spieker-Kiepert Triangle are perspective with
perspector the External Center of Similitude of the Apollonius Circle and the
Nine-Point Circle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Incentral Triangle are perspective with perspector
the Perspector of Triangle ABC and the Intouch Triangle of the Incentral
Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Medial Triangle are perspective with perspector the
Nagel Point. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Orthic Triangle are perspective with perspector the
Perspector of Triangle ABC and the Intouch Triangle of the Orthic Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Symmedial Triangle are perspective with perspector
the Perspector of Triangle ABC and the Intouch Triangle of the Symmedial
Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Intouch Triangle are perspective with perspector the
Congruent Isoscelizers Point. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Extouch Triangle are perspective with perspector the
Perspector of Triangle ABC and the Intouch Triangle of the Extouch Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Pedal Triangle of the Incenter are perspective with
perspector the Congruent Isoscelizers Point. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Pedal Triangle of the Circumcenter are perspective
with perspector the Nagel Point. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Pedal Triangle of the Orthocenter are perspective
with perspector the Perspector of Triangle ABC and the Intouch Triangle of
the Orthic Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Pedal Triangle of the Bevan Point are perspective
with perspector the Perspector of Triangle ABC and the Intouch Triangle of
the Extouch Triangle. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Malfatti Central Triangle are perspective with
perspector the First Ajima-Malfatti Point. Triangle ABC and the Inner Johnson Triangle of
the Soddy Circles of the Lucas Central Triangle are perspective with
perspector the Inner Kenmotu Point. Triangle ABC and the Inner Johnson Triangle of
the Lucas Circles of the Intouch Triangle are perspective with perspector the
Center of the Inner Soddy Circle. Triangle ABC and the Inner Johnson Triangle of
the Lucas Circles of the Pedal Triangle of the Incenter are perspective with
perspector the Center of the Inner Soddy Circle. Triangle ABC and the Inner Johnson Triangle of
the Neuberg Circles of the First Brocard Triangle are perspective with
perspector the Incenter. The Euler Triangle and the Inner Johnson Triangle
of the Excircles of the Medial Triangle are homothetic with homothetic center
the Nine-Point Center. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Orthic Triangle are perspective with
perspector the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Anticomplementary Triangle are homothetic
with homothetic center the Skordev Point. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Orthocenter are
perspective with perspector the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Circumcenter are
homothetic with homothetic center the Nine-Point Center. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Orthocenter are
perspective with perspector the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Orthocenter are
homothetic with homothetic center the Skordev Point. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the de Longchamps
Point are perspective with perspector the Orthocenter. The Euler Triangle and the Inner Johnson Triangle
of the Excircles of the Circumcevian Triangle of the Circumcenter are
homothetic with homothetic center the Centroid. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Circum-Orthic Triangle are perspective with
perspector the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Triangle of the reflections are perspective
with perspector the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Johnson Triangle are homothetic with
homothetic center the Center of the Orthocentroidal Circle. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Inner Johnson-Yff Triangle are homothetic
with homothetic center the Center of the Outer Johnson-Yff Circle. The Euler Triangle and the Inner Johnson
Triangle of the Excircles of the Outer Johnson-Yff Triangle are homothetic
with homothetic center the Center of the Inner Johnson-Yff Circle. The Euler Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Euler Triangle are perspective with
perspector the Midpoint of the Gergonne Point and the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Neuberg Circles of the Euler Triangle are perspective with
perspector the Midpoint of the Incenter and the Orthocenter. The Euler Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the Euler Triangle are
perspective with perspector the Midpoint of the Incenter and the Orthocenter.
The Euler Triangle and the Inner Johnson
Triangle of the Triad of the Hexyl Circles of the Corner Triangles of the
Tangential Triangle are perspective with perspector the Circumcenter. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Incentral Triangle are perspective with
perspector the First Feuerbach Point. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Second Feuerbach
Point are perspective with perspector the Second Feuerbach Point. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are perspective with
perspector the Nine-Point Center. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Second Feuerbach
Point are perspective with perspector the Second Feuerbach Point. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
perspective with perspector the Nine-Point Center. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Circumcevian Triangle of the Second
Feuerbach Point are perspective with perspector the Second Feuerbach Point. The Feuerbach Triangle and the Inner Johnson
Triangle of the Excircles of the Apollonius Triangle are perspective with
perspector the Spieker Center. The Feuerbach Triangle and the Inner Johnson
Triangle of the Triad of the Incircles of the Triangulation Triangles of the
Second Feuerbach Point are perspective with perspector the Second Feuerbach
Point. The Intangents Triangle and the Inner Johnson
Triangle of the Soddy Circles are perspective with perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Incentral Triangle are perspective with
perspector the Internal Center of Similitude of the Incircle and the
Circumcircle. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Intouch Triangle are perspective with
perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Tangential Triangle are homothetic with
homothetic center the Internal Center of Similitude of the Incircle and the
Circumcircle. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Incenter are
perspective with perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Circumcenter are
homothetic with homothetic center the Internal Center of Similitude of the
Incircle and the Circumcircle. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Bevan Point are
perspective with perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Extangents Triangle are homothetic with
homothetic center the Internal Center of Similitude of the Incircle and the
Circumcircle. The Intangents Triangle and the Inner Johnson
Triangle of the Excircles of the Hexyl Triangle are perspective with
perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Inner Johnson-Yff Triangle are
perspective with perspector the Incenter. The Intangents Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Outer Johnson-Yff Triangle are
perspective with perspector the Incenter. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Incentral Triangle are perspective with
perspector the Internal Center of Similitude of the Incircle and the
Circumcircle. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Orthic Triangle are homothetic with
homothetic center the Clawson Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Extouch Triangle are perspective with
perspector the Bevan Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are perspective with
perspector the Bevan Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Tangential Triangle are homothetic with
homothetic center the Internal Center of Similitude of the Incircle and the
Circumcircle. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Orthocenter are
homothetic with homothetic center the Clawson Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Bevan Point are
perspective with perspector the Bevan Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
perspective with perspector the Bevan Point. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Circumcenter are
homothetic with homothetic center the Internal Center of Similitude of the
Incircle and the Circumcircle. The Extangents Triangle and the Inner Johnson
Triangle of the Excircles of the Intangents Triangle are homothetic with
homothetic center the Internal Center of Similitude of the Incircle and the
Circumcircle. The Extangents Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Circumcevian Triangle of the
Circumcenter are perspective with perspector the Bevan Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Excircles of the Medial Triangle are perspective with
perspector the Circumcenter. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Excircles of the Anticomplementary Triangle are perspective
with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Excircles of the Tangential Triangle are perspective with
perspector the Circumcenter. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Neuberg Circles of the Anticomplementary Triangle are
perspective with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Neuberg Circles of the Antipedal Triangle of the Orthocenter
are perspective with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the Anticomplementary Triangle
are perspective with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the Antipedal Triangle of the
Orthocenter are perspective with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the First Brocard Triangle are
perspective with perspector the Nagel Point. The Fuhrmann Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the Inner Gallatly-Kiepert
Triangle are perspective with perspector the Nagel Point. The Mid-Arc Triangle and the Inner Johnson
Triangle of the Soddy Circles are perspective with perspector the Incenter of
the Intouch Triangle. The Mid-Arc Triangle and the Inner Johnson Triangle
of the Neuberg Circles are perspective with perspector the Incenter. The Mid-Arc Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles are perspective with perspector the
Incenter. The Mid-Arc Triangle and the Inner Johnson Triangle
of the Excircles of the Incentral Triangle are perspective with perspector
the Incenter. The Mid-Arc Triangle and the Inner Johnson
Triangle of the Excircles of the Intouch Triangle are perspective with
perspector the Incenter of the Intouch Triangle. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Orthic Triangle are perspective with
perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Nine-Point Center are
perspective with perspector the Circumcenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Outer Fermat Point
are perspective with perspector the First Isodynamic Point. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Inner Fermat Point
are perspective with perspector the Second Isodynamic Point. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are perspective with
perspector the Evans Perspector. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Orthocenter are
perspective with perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Orthocenter are
perspective with perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Nine-Point Center are
homothetic with homothetic center the Centroid. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
perspective with perspector the Evans Perspector. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the de Longchamps
Point are perspective with perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Circum-Orthic Triangle are perspective with
perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Euler Triangle are perspective with
perspector the Orthocenter. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Outer Fermat Triangle are perspective with
perspector the Second Isodynamic Point. The Reflection Triangle and the Inner Johnson
Triangle of the Excircles of the Inner Fermat Triangle are perspective with
perspector the First Isodynamic Point. The First Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Second Brocard Triangle are perspective with
perspector the Centroid. The Second Brocard Triangle and the Inner
Johnson Triangle of the Excircles of the Tangential Triangle are perspective
with perspector the Symmedian Point. The Second Brocard Triangle and the Inner
Johnson Triangle of the Excircles of the Antipedal Triangle of the
Circumcenter are perspective with perspector the Symmedian Point. The Second Brocard Triangle and the Inner
Johnson Triangle of the Excircles of the First Brocard Triangle are
perspective with perspector the Centroid. The Second Brocard Triangle and the Inner
Johnson Triangle of the Excircles of the Inner Gallatly-Kiepert Triangle are
perspective with perspector the Centroid. The Third Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Anticomplementary Triangle are perspective
with perspector the Perspector of the Symmedial Triangle and the Anticomplementary
Triangle. The Third Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Orthocenter are
perspective with perspector the Perspector of the Symmedial Triangle and the
Anticomplementary Triangle. The Third Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Neuberg Triangle are perspective with
perspector the Orthocenter. The Third Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Outer Gallatly-Kiepert Triangle are
perspective with perspector the Perspector of the Symmedial Triangle and the
Anticomplementary Triangle. The Third Brocard Triangle and the Inner Johnson
Triangle of the Excircles of the Inner Lemoine-Kiepert Triangle are
perspective with perspector the Orthocenter. The Yff Central Triangle and the Inner Johnson
Triangle of the Soddy Circles are homothetic with homothetic center the Yff
Center of Conguence. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Intouch Triangle are homothetic with
homothetic center the Yff Center of Conguence. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Yff Center of
Conguence are perspective with perspector the Congruent Isoscelizers Point. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are homothetic with
homothetic center the Congruent Isoscelizers Point. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Incenter are
homothetic with homothetic center the Yff Center of Conguence. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
homothetic with homothetic center the Congruent Isoscelizers Point. The Yff Central Triangle and the Inner Johnson
Triangle of the Excircles of the Circum-Incentral Triangle are homothetic
with homothetic center the Dimovski Point. The de Villiers Triangle and the Inner Johnson
Triangle of the Incenter-Excenter Circles are perspective with perspector the
Incenter. The de Villiers Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Yff Center of
Conguence are perspective with perspector the Incenter. The de Villiers Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Congruent
Isoscelizers Point are perspective with perspector the Incenter. The de Villiers Triangle and the Inner Johnson
Triangle of the Neuberg Circles of the Malfatti Central Triangle are
perspective with perspector the Radical Center of the Malfatti Circles. The de Villiers Triangle and the Inner Johnson
Triangle of the Reflected Neuberg Circles of the Malfatti Central Triangle
are perspective with perspector the Radical Center of the Malfatti Circles. The Malfatti Squares Triangle and the Inner
Johnson Triangle of the Excircles of the Pedal Triangle of the Symmedian
Point are homothetic with homothetic center the Centroid. The Lucas Central Triangle and the Inner Johnson
Triangle of the Excircles of the Tangential Triangle are perspective with
perspector the Inner Kenmotu Point. The Lucas Central Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Circumcenter are
perspective with perspector the Inner Kenmotu Point. The Lucas Central Triangle and the Inner Johnson
Triangle of the Excircles of the Circumcevian Triangle of the Circumcenter
are perspective with perspector the Circumcenter. The Lucas Central Triangle and the Inner Johnson
Triangle of the Excircles of the Inner Lucas Triangle are perspective with
perspector the Center of the Inner Lucas Circle. The Lucas Central Triangle and the Inner Johnson
Triangle of the Triad of the Circumcircles of the Triangulation Triangles of
the First Isodynamic Point are perspective with perspector the Circumcenter. The Inner Lucas Triangle and the Inner Johnson
Triangle of the Excircles of the Lucas Central Triangle are perspective with
perspector the Center of the Inner Lucas Circle. The Neuberg Triangle and the Inner Johnson
Triangle of the Excircles of the Medial Triangle are perspective with
perspector the Circumcenter. The Neuberg Triangle and the Inner Johnson
Triangle of the Excircles of the Tangential Triangle are perspective with
perspector the Circumcenter. The Neuberg Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Third Power Point
are perspective with perspector the Center of the Brocard Circle. The Neuberg Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Third Power Point are
homothetic with homothetic center the Symmedian Point. The Hexyl Triangle and the Inner Johnson
Triangle of the Soddy Circles are homothetic with homothetic center the
Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Intouch Triangle are homothetic with
homothetic center the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Schiffler Point are
perspective with perspector the Circumcenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are homothetic with
homothetic center the Circumcenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Mittenpunkt are
perspective with perspector the Bevan Point. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Clawson Point are
perspective with perspector the Orthocenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Pedal Triangle of the Incenter are
homothetic with homothetic center the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
homothetic with homothetic center the Circumcenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Bevan Point are
perspective with perspector the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Circumcevian Triangle of the Circumcenter
are perspective with perspector the Bevan Point. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Intangents Triangle are perspective with
perspector the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Excircles of the Second Spieker-Kiepert Triangle are
perspective with perspector the Orthocenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Inner Johnson-Yff Triangle are
homothetic with homothetic center the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Soddy Circles of the Outer Johnson-Yff Triangle are homothetic
with homothetic center the Incenter. The Hexyl Triangle and the Inner Johnson
Triangle of the Neuberg Circles of the Circumcevian Triangle of the
Circumcenter are perspective with perspector the Bevan Point. The Hexyl Triangle and the Inner Johnson Triangle
of the Reflected Neuberg Circles of the Circumcevian Triangle of the
Circumcenter are perspective with perspector the Bevan Point. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Incentral Triangle are perspective with
perspector the Internal Center of Similitude of the Apollonius Circle and the
Incircle. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Symmedial Triangle are perspective with
perspector the Danneels-Apollonius Prespector. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Cevian Triangle of the Apollonius Point are
perspective with perspector the Apollonius Point. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Excentral Triangle are perspective with
perspector the Center of the Apollonius Circle. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Anticevian Triangle of the Apollonius Point
are perspective with perspector the Apollonius Point. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Antipedal Triangle of the Incenter are
perspective with perspector the Center of the Apollonius Circle. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Circumcevian Triangle of the Apollonius
Point are perspective with perspector the Apollonius Point. The Apollonius Triangle and the Inner Johnson
Triangle of the Excircles of the Feuerbach Triangle are perspective with
perspector the Spieker Center. The Apollonius Triangle and the Inner Johnson
Triangle of the Triad of the Incircles of the Triangulation Triangles of the
Apollonius Point are perspective with perspector the Apollonius 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 Level
The 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. Thanks
The figures in this note are produced by using the program C.a.R.
(Compass and Ruler), an amazing program created by Rene Grothmann. The
Grothmann's program is available for download in the Web: Rene Grothmann's C.a.R.. It is free and open
source. The reader may verify easily the statements of this paper by using
C.a.R. Many thanks to Rene Grothmann for his wonderful program. References
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