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Construction with medial triangle

Source: Sharygin contest. The final raund. 2008. Grade 10. First day. Problem 2

August 31, 2008
geometryincentercircumcircleparallelogramgeometric transformationreflectionratio

Problem Statement

(A.Myakishev) Let triangle A1B1C1 A_1B_1C_1 be symmetric to ABC ABC wrt the incenter of its medial triangle. Prove that the orthocenter of A1B1C1 A_1B_1C_1 coincides with the circumcenter of the triangle formed by the excenters of ABC ABC.
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