Question 63
Given a circle with two fixed points $A$, $B$ on it, another variable point $P$, and a line $r$, the lines $PA$ and $PB$ are drawn and meet $r$ at $C$ and $D$ respectively. Determine two fixed points of $r$, $M$ and $N$, such that the product $CM \cdot DN$ is constant as $P$ varies.