AT-OEMO-REG 2005 Problem 2

Construct the semicircle $h$ with the diameter $AB$ and the midpoint $M$ . Now construct the semicircle $k$ with the diameter $MB$ on the same side as $h$ . Let $X$ and $Y$ be points on $k$ , such that the arc $BX$ is $\frac{3}{2}$ times the arc $BY$ . The line $MY$ intersects the line $BX$ in $D$ and the semicircle $h$ in $C$ . Show that $Y$ ist he midpoint of $CD$ .