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TOT 067 1984 Autumn Train J1 <A =60^o or ABC is isosceles

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August 24, 2019
geometryangle bisectorisosceles

Problem Statement

In triangle ABCABC the bisector of the angle at BB meets ACAC at DD and the bisector of the angle at CC meets ABAB at EE. These bisectors intersect at OO and the lengths of ODOD and OEOE are equal. Prove that either ∠BAC=60o\angle BAC = 60^o or triangle ABCABC is isosceles.
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