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