Chords chords chords

In the circumference of a circle of radius rr, two points are chosen with a uniform distribution. The probability that the length of the chord between these two points is less than rr is ab \frac{ a}{b} for coprime positive integers a,ba, b .

Find a+3ba+3b.

This problem was from CB Paul Science quiz (Stage round) where it is expected to be solved in 40 seconds.
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