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.

**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

1999-05-25