# AIME 2015 Problem 11

Geometry Level 4

The circumcircle of acute $$\Delta ABC$$ has center $$O$$. The line passing through point $$O$$ perpendicular to $$OB$$ intersects lines $$AB$$ and $$BC$$ and $$P$$ and $$Q$$, respectively. Also $$AB=5$$, $$BC=4$$, $$BQ=4.5$$, and $$BP=\dfrac{m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

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