Antihomologous Points

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.