College Geometry: Gergonne Point, Online Education

Problem 687: Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines. Level: High School, SAT, College Geometry

The figure shows a triangle ABC with the excircles EA, EB, and EC tangent to the extension of sides at the points A1, A2, B1, B2, C1, and C2. Lines CA1 and BA2 meet at A3, AB1 and CB2 meet at B3, BC1 and AC2 meet at C3. Prove that lines AA3, BB3, and CC3 are concurrent.

Three Excircles, Tangent, Concurrent lines

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