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if <A is obtuse, then AB = AC, when A-bisector =(A-altitude + A-median) /2

Source: Sharygin 2006 IX- X CR 12

August 23, 2019
altitudemedianangle bisectorgeometryisosceles

Problem Statement

In the triangle ABCABC, the bisector of angle AA is equal to the half-sum of the height and median drawn from vertex AA. Prove that if ∠A\angle A is obtuse, then AB=ACAB = AC.
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