KöMaL 2015 B4738

$C$ is an arbitrary point of a circle $k$ of diameter $AB$ , different from $A$ and $B$ . Drop a perpendicular from $C$ onto diameter $AB$ . The foot of the perpendicular on line segment $AB$ is $D$ , and the other intersection with the circle $k$ is $E$ . The circle of radius $CD$ centred at $C$ intersects circle $k$ at points $P$ and $Q$ . Let $M$ denote the intersection of line segments $CE$ and $PQ$ . Dertermine the value of $\frac{PM}{PE} + \frac{QM}{QE}$ .