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Iran geometry

Source: Iranian TST 2019, third exam day 2, problem 4

April 15, 2019
geometrygeometric transformationreflectioncircumcircle

Problem Statement

Given an acute-angled triangle ABCABC with orthocenter HH. Reflection of nine-point circle about AHAH intersects circumcircle at points XX and YY. Prove that AHAH is the external bisector of ∠XHY\angle XHY.
Proposed by Mohammad Javad Shabani
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