Two points which are Collinear with respect to a Similitude Center but are not Homologous Points.
Four interesting theorems from Johnson (1929) follow.
- 1. Two pairs of antihomologous points form inversely similar triangles with the Homothetic Center.
- 2. The Product of distances from a Homothetic Center to two antihomologous points is a constant.
- 3. Any two pairs of points which are antihomologous with respect to a Similitude Center lie on a
Circle.
- 4. The tangents to two Circles at antihomologous points make equal Angles with
the Line through the points.
See also Homologous Points, Homothetic Center, Similitude Center
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 19-21, 1929.
© 1996-9 Eric W. Weisstein
1999-05-25