Problem

Source: Lithuania NMO 2010

Tags: geometry, incenter, circumcircle, inradius, perpendicular bisector, geometry unsolved



Let $I$ be the incenter of a triangle $ABC$. $D,E,F$ are the symmetric points of $I$ with respect to $BC,AC,AB$ respectively. Knowing that $D,E,F,B$ are concyclic,find all possible values of $\angle B$.