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perimeter of a triangle equal to side of another triangle

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P11

August 2, 2018
geometryperimeter

Problem Statement

Let HH be the orthocenter of an acute-angled triangle ABCBC. The perpendicular bisector to segment BHBH meets BABA and BCBC at points A0,C0A_0, C_0 respectively. Prove that the perimeter of triangle A0OC0A_0OC_0 (OO is the circumcenter of triangle ABCABC) is equal to ACAC.
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