2011 AIME II Problem 10

A circle with center O has radius 25. Chord \overline{A B} of length 30 and chord
\overline{C D} of length 14 intersect at point P. The distance between the midpoints of the
two chords is 12 . The quantity O P^{2} can be represented as \frac{m}{n}, where m and n are relatively
prime positive integers. Find the remainder when m+n is divided by 1000 .