2011 AIME II Problems/Problem 10

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Problem:

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 expressed as $\frac{m}{n}$, where m and n are relatively prime positive integers. Find the remainder when m + n is divided by 1000.

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