2021 AMC 12A Problem 17

Trapezoid ABCD has \overline{AB}\parallel\overline{CD},BC=CD=43, and \overline{AD}\perp\overline{BD}. Let O be the intersection of the diagonals \overline{AC} and \overline{BD}, and let P be the midpoint of \overline{BD}. Given that OP=11, the length of 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?

\textbf{(A) }65 \qquad \textbf{(B) }132 \qquad \textbf{(C) }157 \qquad \textbf{(D) }194\qquad \textbf{(E) }215

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.