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O, I and orthocenter of intouch triangle collinear

Source: Kürschák 1997, problem 2

July 15, 2014
geometrycircumcircleincentergeometry unsolved

Problem Statement

The center of the circumcircle of △ABC\triangle ABC is OO. The incenter of the triangle is II, and the intouch triangle is A1B1C1A_1B_1C_1. Let H1H_1 be the orthocenter of △A1B1C1\triangle A_1B_1C_1. Prove that OO, II, and H1H_1 are collinear.
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