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Normal geometry

Source: 2020 China Second Round (A) P1

September 13, 2020
geometryincenter

Problem Statement

In triangle ABC,ABC, AB=BC,AB=BC, and let II be the incentre of △ABC.\triangle ABC. MM is the midpoint of segment BI.BI. PP lies on segment AC,AC, such that AP=3PC.AP=3PC. HH lies on line PI,PI, such that MH⊥PH.MH\perp PH. QQ is the midpoint of the arc ABAB of the circumcircle of △ABC\triangle ABC. Prove that BH⊥QH.BH\perp QH.
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