Problem

Source: V.A. Yasinsky Geometry Olympiad 2019 VIII-IX advanced p1 [Ukraine]

Tags: angles, geometry, inradius, Angle Chasing



It is known that in the triangle $ABC$ the distance from the intersection point of the angle bisector to each of the vertices of the triangle does not exceed the diameter of the circle inscribed in this triangle. Find the angles of the triangle $ABC$. (Grigory Filippovsky)