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Centers in a isosceles triangle

Source: 2021China South East Mathematical Olympiad Grade10 P2

July 28, 2021
geometry

Problem Statement

In △ABC\triangle ABC,AB=AC>BCAB=AC>BC, point O,HO,H are the circumcenter and orthocenter of △ABC\triangle ABC respectively,GG is the midpoint of segment AHAH , BEBE is the altitude on ACAC . Prove that if OE∥BCOE\parallel BC, then HH is the incenter of △GBC\triangle GBC.
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