Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

Tags: geometry, circle, chord



In circle with radius $10$, point $M$ is on chord $PQ$ such that $PM=5$ and $MQ=10$. Through point $M$ we draw chords $AB$ and $CD$, and points $X$ and $Y$ are intersection points of chords $AD$ and $BC$ with chord $PQ$ (see picture), respectively. If $XM=3$ find $MY$