Let A, B, and C be circles with equal radii and tangent externally
pairwise. Let O be the circle tangent externally to A, B, and C and
P any point on O. For X∈{A,B,C}, let X' be one of the two points
on X such that line PX' is tangent to X and let x = |PX'|.

Prove that (a+b-c)(b+c-a)(c+a-b) = 0.