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Side Length of a Triangle

Source: Aime 2005b, #14

November 14, 2005
trigonometrygeometrycircumcircleanalytic geometrynumber theoryrelatively primetrig identities

Problem Statement

In triangle ABCABC, AB=13AB=13, BC=15BC=15, and CA=14CA=14. Point DD is on BC‾\overline{BC} with CD=6.CD=6. Point EE is on BC‾\overline{BC} such that ∠BAE≅∠CAD.\angle BAE\cong \angle CAD. Given that BE=pqBE=\frac pq where pp and qq are relatively prime positive integers, find q.q.
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