2011 AIME II Problem 10

A circle with center O has radius 25. Chord \overline{AB} of length 30 and chord \overline{CD} of length 14 intersect at point P. The distance between the midpoints of the two chords is 12. The quantity OP^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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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