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ABC and A1B1C1 are congruent

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September 18, 2010
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Problem Statement

In triangle ABC,OABC, O is the circumcenter, HH is the orthocenter. Construct the circumcircles of triangles CHB,CHACHB, CHA and AHBAHB, and let their centers be A1,B1,C1A_1, B_1, C_1, respectively. Prove that triangles ABCABC and A1B1C1A_1B_1C_1 are congruent, and their nine-point circles coincide.
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