MathDB

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 where

m+n

is divided by 1000.

Problem Statement