Problem

Source: china mathematical olympiad cmo 2005 final round - Problem 2

Tags: geometry, inequalities, conics, trigonometry, China



A circle meets the three sides BC,CA,AB of a triangle ABC at points D1,D2;E1,E2;F1,F2 respectively. Furthermore, line segments D1E1 and D2F2 intersect at point L, line segments E1F1 and E2D2 intersect at point M, line segments F1D1 and F2E2 intersect at point N. Prove that the lines AL,BM,CN are concurrent.