KURSCHAK 1997 Problem 2

The center of the circumcircle of $\triangle ABC$ is $O$ . The incenter of the triangle is $I$ , and the intouch triangle is $A_1B_1C_1$ . Let $H_1$ be the orthocenter of $\triangle A_1B_1C_1$ . Prove that $O$ , $I$ , and $H_1$ are collinear.