# Day 18: An Incredible Result

Geometry Level 4

A triangle $$ABC$$ has a right angle at $$B$$. A semicircle is inscribed within on the side $$BC$$ and its diameter is equal to $$AB$$.

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

This problem is part of the set Advent Calendar 2014.

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