MathNet 2015-part-02 — 191 problems (EN–VI) Question 163

Let $ABC$ be a triangle with all angles acute, and $H$ its orthocentre. The bisectors of $\widehat{ABH}$ and $\widehat{ACH}$ meet at a point $I$. Show that $I$ is collinear with the midpoints of $[BC]$ and of $[AH]$.