# 2015 Mock AIME I Problem 3: Intersection of Circles

Level pending

Let $$A,B,C$$ be points in the plane such that $$AB=25$$, $$AC=29$$, and $$\angle BAC<90^\circ$$. Semicircles with diameters $$\overline{AB}$$ and $$\overline{AC}$$ intersect at a point $$P$$ with $$AP=20$$. Find the maximum possible length of line segment $$\overline{BC}$$.

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