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.