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1400
Common Chord
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geometrycirclescoordinate geometry
Two circles, C1C_1 and C2C_2, intersect at points PP and QQ. The radius of C1C_1 is 5 and the radius of C2C_2 is 12. The distance between the centers of the two circles is exactly 13. If the length of the common chord PQPQ can be expressed as a fraction in simplest form ab\frac{a}{b}, what is a+ba + b?

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