CAPS 2015 Problem 5

Let $ABC$ be an acute triangle, which is not equilateral. Denote by $O$ and $H$ its circumcenter and orthocenter, respectively. The circle $k$ passes through $B$ and touches the line $AC$ at $A$ . The circle $l$ with center on the ray $BH$ touhes the line $AB$ at $A$ . The circles $k$ and $l$ meet in $X$ ( $X\ne A$ ). Show that $\angle HXO=180^\circ-\angle BAC$ .

Proposed by Josef Tkadlec