IMAS 2019–2020 Junior Division Round 2 Question 12

In the figure below, points $P$ and $Q$ lie on side $BC$ of triangle $ABC$ and point $M$ is the midpoint of side $AB$. If $BP=CQ=9$ cm, $AC=20$ cm and $PM\perp MQ$, then what is the length, in cm, of side $BC$?