IrMO 2015 Problem 8

In triangle $\triangle ABC$ , the angle $\angle BAC$ is less than $90^o$ . The perpendiculars from $C$ on $AB$ and from $B$ on $AC$ intersect the circumcircle of $\triangle ABC$ again at $D$ and $E$ respectively. If $|DE| =|BC|$ , find the measure of the angle $\angle BAC$ .