# My 10th problem

Geometry Level 5

Triangle $$AB_0C_0$$ has side lengths $$AB_0 = 12$$, $$B_0C_0 = 17$$, and $$C_0A = 25$$. 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 $$\triangle AB_nC_n \sim \triangle B_{n-1}C_nC_{n-1} \sim \triangle AB_{n-1}C_{n-1}$$. The area of the union of all triangles $$B_{n-1}C_nB_n$$ for $$n\geq1$$ can be expressed as $$\tfrac pq$$, where $$p$$ and $$q$$ are relatively prime positive integers. Find $$q$$.

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