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Sum of lengths

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April 26, 2022

Problem Statement

Let triangle A1BCA_1BC have sides A1B=5A_1B=5, A1C=12A_1C=12, and BC=13BC=13. For all natural numbers ii, let BiB_i be the foot of the altitude from AiA_i to BCBC, let A2iA_{2i} be the foot of the altitude from BiB_i to A1BA_1B, and let A2i+1A_{2i+1} be the foot of the altitude from BiB_i to A1CA_1C. ∑i=17AiBi=pq \sum_{i=1}^{7}A_iB_i = \frac{p}{q} Find p+qp+q.
2022 CCA Math Bonanza Individual Round #13
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