Let ABC be a triangle inscribed in a circle of radius O. The angle bisectors AD,BE,CF are concurrent at I. The points M,N,P are respectively on EF,FD, and DE such that IM,IN,IP are perpendicular to BC,CA,AB respectively. Prove that the three lines AM,BN,CP are concurrent at a point on OI.Nguyễn Minh Hà geometryconcurrentincentercircumcircle