Question 25
A pentagon $ABCDE$ is inscribed in a circle of radius $10$ such that $BC$ is parallel to $AD$ and $AD$ intersects $CE$ at $M$. The tangents to this circle at $B$ and $E$ meet the extension of $DA$ at a common point $P$. Suppose $PB=PE=24$ and $\angle BPD=30^\circ$. Find $BM$.