MathNet 2018-part-01 — 181 problems (EN–VI) Question 117

A point $O$ is chosen inside a triangle $ABC$ so that the lengths of the 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 $ABC$.