## 2013 AIME I Problem 13

2013 AIME I 13. Triangle $AB_0C_0$ has side lengths $AB_0 = 12$$B_0C_0 = 17$$C_0A = 25$. For each positive integer $n$, points $B_n$ and $C_n$ are located on $\overline{AB_{n-1}}$ and $\overline{AC_{n-1}}$ respectively, creating three similar triangles $\Delta AB_nC_n \sim \Delta B_{n-1}C_nC_{n-1} \sim \Delta AB_{n-1}C_{n-1}$. The area of the union of all triangles $B_{n-1}C_nB_n$ for $n \geq 1$ can be expressed as $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $q$.