Three Chords & The Truth

Geometry Level 4

Segments PA\overline{PA}, PB\overline{PB}, and PC\overline{PC} are all chords of the same circle, Γ\Gamma, such that PA=5PA=5, PB=8PB=8, and PC=3PC=3. In addition, APBBPC.\angle APB \cong \angle BPC. The area of Γ\Gamma can be written as abπ\frac{a}{b}\pi, where aa and bb are positive, coprime integers. Find a+ba+b.

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