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Excribed circles and orthocenters

Source: Romania TST 1991 Test 2 P1

February 20, 2014
geometryincentercircumcircleparallelogramgeometric transformationreflectiongeometry proposed

Problem Statement

In a triangle A1A2A3A_1A_2A_3, the excribed circles corresponding to sides A2A3A_2A_3, A3A1A_3A_1, A1A2A_1A_2 touch these sides at T1T_1, T2T_2, T3T_3, respectively. If H1H_1, H2H_2, H3H_3 are the orthocenters of triangles A1T2T3A_1T_2T_3, A2T3T1A_2T_3T_1, A3T1T2A_3T_1T_2, respectively, prove that lines H1T1H_1T_1, H2T2H_2T_2, H3T3H_3T_3 are concurrent.
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