Question 42
Let $M$ be a point on a circle $k$. A circle $k_{1}$ with center $M$ meets $k$ at points $C$ and $D$. A chord $AB$ of $k$ is tangent to $k_{1}$ at point $H$. Prove that the line $CD$ bisects the segment $MH$ if and only if $AB$ is a diameter of $k$.