MathDB
BMT 2022 Guts #16

Source:

August 31, 2023
geometry

Problem Statement

Let triangle △ABC\vartriangle ABC be a triangle with AB=5AB = 5, BC=7BC = 7, and CA=8CA = 8, and let II be the incenter of △ABC\vartriangle ABC. Let circle CAC_A denote the circle with center AA and radius AI‾\overline{AI}, denote CBC_B and circle CCC_C similarly. Besides all intersecting at II, the circles CAC_A,CBC_B,CCC_C also intersect pairwise at FF, GG, and HH. Compute the area of triangle △FGH\vartriangle FGH.
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