Let ABC be a triangle and let O be its circumcentre. The internal and external bisectrices of the angle BAC meet the line BC at points D and E, respectively. Let further M and L respectively denote the midpoints of the segments BC and DE. The circles ABC and ALO meet again at point N. Show that the angles BAN and CAM are equal. geometrysymmedianequal anglescirclescircumcircleangle bisector