In a triangle A1A2A3, the excribed circles corresponding to sides A2A3, A3A1, A1A2 touch these sides at T1, T2, T3, respectively. If H1, H2, H3 are the orthocenters of triangles A1T2T3, A2T3T1, A3T1T2, respectively, prove that lines H1T1, H2T2, H3T3 are concurrent. geometryincentercircumcircleparallelogramgeometric transformationreflectiongeometry proposed