Problem 686: Triangle, Three Excircles, Tangency points,
Tangent lines, Semi-perimeter, Congruence. Level: High School, SAT,
The figure shows a triangle ABC with
semiperimeter s and the excircles EA, EB, and EC tangent to the sides at the points A', B', C',
A1, A2, B1, B2, C1,
and C2. Prove that s = AA1 = AA2 = BB1
= BB2 = CC1 = CC2.