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IGO 2021 P1

Source: igo 2021 intermediate p1

December 30, 2021
geometry

Problem Statement

Let ABCABC be a triangle with AB=ACAB = AC. Let HH be the orthocenter of ABCABC. Point EE is the midpoint of ACAC and point DD lies on the side BCBC such that 3CD=BC3CD = BC. Prove that BE⊥HDBE \perp HD.
Proposed by Tran Quang Hung - Vietnam
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