CONO-SUR 2016 Problem 5

Let $ABC$ be a triangle inscribed on a circle with center $O$ . Let $D$ and $E$ be points on the sides $AB$ and $BC$ ,respectively, such that $AD = DE = EC$ . Let $X$ be the intersection of the angle bisectors of $\angle ADE$ and $\angle DEC$ . If $X \neq O$ , show that, the lines $OX$ and $DE$ are perpendicular.