BG-MO 2002 Problem 4

Let $I$ be the incenter of a non-equilateral triangle $ABC$ and $T_1$ , $T_2$ , and $T_3$ be the tangency points of the incircle with the sides $BC$ , $CA$ and $AB$ , respectively. Prove that the orthocenter of triangle $T_1T_2T_3$ lies on the line $OI$ , where $O$ is the circumcenter of triangle $ABC$ .

Proposed by Georgi Ganchev