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equal segments by excircles (2021 Adygea Teachers' Geometry Olympiad p3)

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March 31, 2021
geometryexcircle

Problem Statement

In a triangle, one excircle touches side ABAB at point C1C_1 and the other touches side BCBC at point A1A_1. Prove that on the straight line A1C1A_1C_1 the constructed excircles cut out equal segments.
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