Question 17
Trapezoid $ABCD$ has $AB \parallel CD,$ $BC = CD = 43,$ and $AD \perp BD.$ Let $O$ be the intersection of the diagonals $AC$ and $BD,$ and let $P$ be the midpoint of $BD.$ Given that $OP = 11,$ the length $AD$ can be written in the form $m\sqrt n,$ where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. What is $m + n?$