# Three Chords & The Truth

Geometry Level 4

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

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