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
Problem
Source: Bulgarian MO 2002 4th round day 2 problem 1
Tags: geometry, incenter, circumcircle, Euler, geometry unsolved