Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 3.1

Tags: angles, geometry, circumcircle



Let $\vartriangle ABC$ be such that $\angle BAC$ is acute. The line perpendicular on side $AB$ from $C$ and the line perpendicular on $AC$ from $B$ intersect the circumscribed circle of $\vartriangle ABC$ at $D$ and $E$ respectively. If $DE = BC$ , calculate $\angle BAC$.