MathNet 2014 Question 72

Let $H$ be orthocenter of the triangle $ABC$. A certain circle with diameter $AC$ intersects circumcircle of the triangle $ABH$ at point $K$ which is different from $A$. Prove that intersection point of $CK$ and $BH$ divides the line segment $BH$ into equal parts.

(proposed by B. Battsengel)