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area of quadr. wanted, 13-14-15 triangle, incenter excenter 2019 BMT Team 13

Source:

January 5, 2022
geometryincentercircumcircle

Problem Statement

Triangle △ABC\vartriangle ABC has AB=13AB = 13, BC=14BC = 14, and CA=15CA = 15. △ABC\vartriangle ABC has incircle γ\gamma and circumcircle ω\omega. γ\gamma has center at II. Line AIAI is extended to hit ω\omega at PP. What is the area of quadrilateral ABPCABPC?
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