Question 139
A trapezium $ABCD$ with $AB \parallel DC$ and $|AB| \lt |DC|$ is inscribed in a circle, centre $O$. The diagonals $AC$ and $BD$ are mutually perpendicular at $P$. If $E$ is the midpoint of $AB$ and $F$ is the midpoint of $DC$, prove $|OF| = |PE|$.