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An isosceles triangle

Source: All Russian 2017,grade 9,day 2,P7

May 1, 2017
circumcircleangle bisectorparallelgeometryIsosceles Triangle

Problem Statement

In the scalene triangle ABCABC,∠ACB=60\angle ACB=60 and Ω\Omega is its cirumcirle.On the bisectors of the angles BACBAC and CBACBA points A′A^\prime,B′B^\prime are chosen respectively such that AB′∥BCAB^\prime \parallel BC and BA′∥ACBA^\prime \parallel AC.A′B′A^\prime B^\prime intersects with Ω\Omega at D,ED,E.Prove that triangle CDECDE is isosceles.(A. Kuznetsov)
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