CR-MO 2019 G2

Let $H$ be the orthocenter and $O$ the circumcenter of the acute triangle $\vartriangle ABC$ . The circle with center $H$ and radius $HA$ intersects the lines $AC$ and $AB$ at points $P$ and $Q$ , respectively. Let point $O$ be the orthocenter of triangle $\vartriangle APQ$ , determine the measure of $\angle BAC$ .