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SMT 2020 Geometry #8

Source:

August 9, 2023
geometry

Problem Statement

Consider an acute angled triangle △ABC\vartriangle ABC with side lengths 77, 88, and 99. Let HH be the orthocenter of ABCABC. Let ΓA\Gamma_A, ΓB\Gamma_B, and ΓC\Gamma_C be the circumcircles of △BCH\vartriangle BCH, △CAH\vartriangle CAH, and △ABH\vartriangle ABH respectively. Find the area of the region ΓA∪ΓB∪ΓC\Gamma_A \cup \Gamma_B \cup \Gamma_C (the set of all points contained in at least one of ΓA\Gamma_A, ΓB\Gamma_B, and ΓC\Gamma_C).
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