College Geometry: Gergonne Point, Online Education

Problem 686: Triangle, Three Excircles, Tangency points, Tangent lines, Semi-perimeter, Congruence. Level: High School, SAT, College Geometry

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.

Triangle with 3 excircles, tangent, congruence

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