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Angle bisector through circumcenter

Source: Sharygin Finals 2017, Problem 8.2

August 4, 2017
geometrycircumcircleperpendicular bisectorangle bisector

Problem Statement

Let HH and OO be the orthocenter and circumcenter of an acute-angled triangle ABCABC, respectively. The perpendicular bisector of BHBH meets ABAB and BCBC at points A1A_1 and C1C_1, respectively. Prove that OBOB bisects the angle A1OC1A_1OC_1.
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