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restore ABC if A, P, W are given

Source: Sharygin Finals 2023 8.7

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023

Problem Statement

The bisector of angle AA of triangle ABCABC meet its circumcircle ω\omega at point WW. The circle ss with diameter AHAH (HH is the orthocenter of ABCABC) meets ω\omega for the second time at point PP. Restore the triangle ABCABC if the points AA, PP, WW are given.
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