Question 62
Tangents from point $P$ to circle $k$ touch the circle at points $A$ and $B$. Let $X$ be any point on the shorter arc $\widehat{A B}$. We denote by $C$ the perpendicular projection of the point $P$ onto the line $A X$ and by $D$ the perpendicular projection of the point $P$ onto the line $B X$. Prove that the line $C D$ passes through some point $Y$, which is independent of the choice of the point $X$ on the arc $\widehat{A B}$.