The incircle of triangle ABC touches sides BC, AC, and AB at D,E, and F respectively. Let ωa,ωb and ωc be the circumcircles of triangles EAF,DBF, and DCE, respectively. The lines DE and DF cut ωa at Ea=E and Fa=F, respectively. Let rA be the line EaFa. Let rB and rC be defined analogously. Show that the lines rA, rB, and rC determine a triangle with its vertices on the sides of triangle ABC. cono surgeometry proposedgeometry