Let ABC be a triangle and D a point on its side BC. Points E,F lie on the lines AB,AC beyond vertices B,C, respectively, such that BE=BD and CF=CD. Let P be a point such that D is the incenter of triangle PEF. Prove that P lies inside the circumcircle Ω of triangle ABC or on it. geometryinternational competitionscircumcircleinteriorsamelengthsincenter