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find point X on BC such that symmetric of orthocenter wrt lies on circumcircle

Source: 2017 Indonedia MO Province P2 q3

December 10, 2020
geometrySymmetricorthocentercircumcircle

Problem Statement

Given triangle ABCABC, the three altitudes intersect at point HH. Determine all points XX on the side BCBC so that the symmetric of HH wrt point XX lies on the circumcircle of triangle ABCABC.
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