Three circles A, B, and C have non-collinear centers, unequal radii, and pairwise the distance between their centers is greater than the sum of their radii.

Let P, Q, and R be the intersections of the external tangents to circles A&B, A&C, and B&C respectively.

Let L and M be the intersections of the internal tangents to circles A&B and A&C respectively.

Prove that P, Q, and R are collinear.

Prove that L, M, and R are collinear.

The first problem, prove P, Q, and R are colinear, is known as Monge's Circle Theorem.

http://mathworld.wolfram.com/MongesCircleTheorem.html

Posted by Brian Smith on 2009-11-07 12:11:10