Question 134
In triangle $\triangle ABC$, the angle $\angle BAC$ is less than $90^\circ$. 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 $\angle BAC$.