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< ABC <= 60^o if longest altitude AD=median BE

Source: 2013 Indonesia MO Province P2 q5 OSP

December 10, 2020
geometrygeometric inequalityangles

Problem Statement

Given an acute triangle ABCABC. The longest line of altitude is the one from vertex AA perpendicular to BCBC, and it's length is equal to the length of the median of vertex BB. Prove that ∠ABC≤60o\angle ABC \le 60^o
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