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Circumcircle geometry

Source: Sharygin geometry olympiad 2015, grade 10, Final Round, Problem 6

July 17, 2018
geometrycircumcircleperpendicular bisector

Problem Statement

Let HH and OO be the orthocenter and the circumcenter of triangle ABCABC. The circumcircle of triangle AOHAOH meets the perpendicular bisector of BCBC at point A1≠OA_1 \neq O. Points B1B_1 and C1C_1 are defined similarly. Prove that lines AA1AA_1, BB1BB_1 and CC1CC_1 concur.
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