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2012 ToT Spring Senior A p5 reflection of angle bisectors, congruent triangles

Source:

March 5, 2020
geometryreflectionangle bisectorcongruent trianglesincircletangent

Problem Statement

Let ℓ\ell be a tangent to the incircle of triangle ABCABC. Let ℓa,ℓb\ell_a,\ell_b and ℓc\ell_c be the respective images of ℓ\ell under reflection across the exterior bisector of ∠A,∠B\angle A,\angle B and ∠C\angle C. Prove that the triangle formed by these lines is congruent to ABCABC.
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