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Geometry Level 5

Let ABCPABCP be a quadrilateral inscribed in a circle Γ\Gamma such that PB=PCPB=PC and BAC\angle BAC is obtuse. Let II be the incenter of triangle ABCABC and suppose that line PIPI intersects again Γ\Gamma at point JJ (JJ belongs to the major arc BCBC). If BJ=10BJ=10, JC=17JC=17 and sinBJC=7785\sin \angle BJC=\frac{77}{85}, then the value of ABAC\frac{AB}{AC} can be written as ab \frac{a}{b} , where aa and bb are coprime positive integers. What is the value of a+ba+b?

Details and assumptions

The order of the vertices is A,B,C,PA, B, C, P . In particular, PP lies on the minor arc of BCBC which contains AA.

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