Mock AIME 4 2006-2007 Problems/Problem 11

Problem

Let $\triangle ABC$ be an equilateral triangle. Two points $D$ and $E$ are chosen on $\overline{AB}$ and $\overline{AC}$ , respectively, such that $AD = CE$ . Let $F$ be the intersection of $\overline{BE}$ and $\overline{CD}$ . The area of $\triangle ABC$ is 13 and the area of $\triangle ACF$ is 3. If $\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}$ , where $p$ , $q$ , and $r$ are relatively prime positive integers, compute $p+q+r$ .

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Mock AIME 4 2006-2007 Problems/Problem 11

Problem

Solution