Day 18: An Incredible Result

Geometry Level 4

A triangle ABCABC has a right angle at BB. A semicircle is inscribed within on the side BCBC and its diameter is equal to ABAB.

If the ratio ABBC\frac{AB}{BC} can be written in the form ab\frac{a}{b} where aa and bb are positive coprime integers, find a+ba+b.

This problem is part of the set Advent Calendar 2014.

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