Mock AIME 2 2006-2007 Problems/Problem 14

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Problem

In triangle ABC, $\displaystyle AB = 308$ and $\displaystyle AC=35.$ Given that $\displaystyle AD$, $\displaystyle BE,$ and $\displaystyle CF,$ intersect at $\displaystyle P$ and are an angle bisector, median, and altitude of the triangle, respectively, compute the length of $\displaystyle BC.$

Problem Source

4everwise thought of this problem after reading the first chapter of Geometry Revisited.

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