Let ABC be a triangle and its circumcircle be ω. Let I be the incentre of the ABC. Let the line BI meet AC at E and ω at M for the second time. The line CI meet AB at F and ω at N for the second time. Let the circumcircles of BFI and CEI meet again at point K. Prove that the lines BN, CM, AK are concurrent. geometrycircumcircleincentre