RMO 2016 D1

Let $ABC$ be an isosceles triangle with $AB=AC.$ Let $\Gamma$ be its circumcircle and let $O$ be the centre of $\Gamma$ . let $CO$ meet $\Gamma$ in $D .$ Draw a line parallel to $AC$ thrugh $D.$ Let it intersect $AB$ at $E.$ Suppose $AE : EB=2:1$ .Prove that $ABC$ is an equilateral triangle.