2013 AIME I Problem 13

2013 AIME I 13. Triangle AB_0C_0 has side lengths AB_0 = 12B_0C_0 = 17C_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.

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