Triangle A B_{0} C_{0} has side lengths A B_{0}=12, B_{0} C_{0}=17, and C_{0} A=25. For each positive integer n, points B_{n} and C_{n} are located on \overline{A B_{n-1}} and \overline{A C_{n-1}}, respectively, creating three similar triangles \triangle A B_{n} C_{n} \sim \triangle B_{n-1} C_{n} C_{n-1} \sim \triangle A B_{n-1} C_{n-1}. The area of the union of all triangles B_{n-1} C_{n} B_{n} for n \geq 1 can be expressed as \frac{p}{q}, where p and q are relatively prime positive integers. Find q.