Let ABC be the triangle in which AB>AC. Circle ωa touches the segment of the BC at point D, the extension of the segment AB towards point B at the point F, and the extension of the segment AC towards point C at the point E. The ray AD intersects circle ωa for second time at point M. Denote the circle circumscribed around the triangle CDM by ω. Circle ω intersects the segment DF at N. Prove that FN>ND. geometrycircumcirclegeometric inequalityexcircle