Let ωa,ωb,ωc be the exscribed circles tangent to the sides a,b,c of a triangle ABC, respectively, Ia,Ib,Ic be the centers of these circles, respectively, Ta,Tb,Tc be the points of contact of these circles to the line BC, respectively. The lines TbIc and TcIb intersect at the point Q. Prove that the center of the circle inscribed in triangle ABC lies on the line TaQ. geometryincenterexcirclesexcircleUkrainian TYM