MathNet 2015-part-07 — 185 problems (EN–VI) Question 18

Let $H, I, O, \Omega$ denote the orthocenter, incenter, circumcenter and circumcircle of a scalene acute triangle $A B C$. Prove that if $\angle B A C=60^{\circ}$ then the circumcenter of $\triangle I H O$ lies on $\Omega$.