BY-MO 2018 Problem 97

A point $O$ is choosen inside a triangle $ABC$ so that the length of segments $OA$ , $OB$ and $OC$ are equal to $15$ , $12$ and $20$ , respectively. It is known that the feet of the perpendiculars from $O$ to the sides of the triangle $ABC$ are the vertices of an equilateral triangle. Find the value of the angle $BAC$ .