RU-ALLRUSSIAN 2017 Problem 97

In the scalene triangle $ABC$ , $\angle ACB=60$ and $\Omega$ is its cirumcirle.On the bisectors of the angles $BAC$ and $CBA$ points $A^\prime$ , $B^\prime$ are chosen respectively such that $AB^\prime \parallel BC$ and $BA^\prime \parallel AC$ . $A^\prime B^\prime$ intersects with $\Omega$ at $D,E$ .Prove that triangle $CDE$ is isosceles.(A. Kuznetsov)