# AIME 2012 Number 15

Geometry Level 5

Triangle $$ABC$$ is inscribed in circle $$\omega$$ with $$AB = 5$$, $$BC = 7$$, and $$AC = 3$$. The bisector of angle $$A$$ meets side $$BC$$ at $$D$$ and circle $$\omega$$ at a second point $$E$$. Let $$\gamma$$ be the circle with diameter $$DE$$. Circles $$\omega$$ and $$\gamma$$ meet at $$E$$ and a second point $$F$$. Then $$AF^2 = \frac mn$$, where m and n are relatively prime positive integers. Find $$m + n$$.

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