Problem

Source: 67 Polish MO 2016 Second Round - Problem 2

Tags: geometry, circumcircle, tangent, bisector, Poland



In acute triangle $ABC$ bisector of angle $BAC$ intersects side $BC$ in point $D$. Bisector of line segment $AD$ intersects circumcircle of triangle $ABC$ in points $E$ and $F$. Show that circumcircle of triangle $DEF$ is tangent to line $BC$.