Question 115
$H$ is the foot of the altitude of vertex $A$ of triangle $ABC$ and $H'$ is the reflection of $H$ with respect to the midpoint of $BC$. If tangents to the circumcircle of triangle $ABC$ at points $B$ and $C$ intersect each other at $X$ and the perpendicular to $XH'$ at $H'$ intersects lines $AB$ and $AC$ at $Y$ and $Z$, respectively, prove that $\angle YXB = \angle ZXC$.