MathNet 2010 — Part 01 Question 73

Given a $\triangle ABC$ with $\angle ACB = 90^\circ$ and altitude $CH$ ($H \in AB$). A circle $k$ touches the segments $BH$ and $CH$, and the circumcircle of $\triangle ABC$. If $D = k \cap BH$, prove that $CD$ bisects $\angle BCH$.