Question 145
In a scalene triangle $ABC$ let $O$ be the circumcenter, $I$ the incenter and $H$ the orthocenter. Let $M$ be the second intersection point of the circle which passes through $O$ and is tangent to $IH$ at $I$, and the circle which passes through $H$ and is tangent to $IO$ at $I$. Show that $M$ lies on the circumcircle of the triangle $ABC$.