2005 AIME II Problems/Problem 14

Problem

In triangle $ABC, AB=13, BC=15,$ and $\displaystyle CA = 14.$ Point $D$ is on $\overline{BC}$ with $CD=6.$ Point $E$ is on $\overline{BC}$ such that $\angle BAE\cong \angle CAD.$ Given that $BE=\frac pq$ where $p$ and $q$ are relatively prime positive integers, find $q.$

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2005 AIME II Problems/Problem 14

Problem

Solution

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