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circle that cuts side of a triangle in 6 points - china 2005

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

January 22, 2005
geometryinequalitiesconicstrigonometryChina

Problem Statement

A circle meets the three sides BC,CA,ABBC,CA,AB of a triangle ABCABC at points D1,D2;E1,E2;F1,F2D_1,D_2;E_1,E_2; F_1,F_2 respectively. Furthermore, line segments D1E1D_1E_1 and D2F2D_2F_2 intersect at point LL, line segments E1F1E_1F_1 and E2D2E_2D_2 intersect at point MM, line segments F1D1F_1D_1 and F2E2F_2E_2 intersect at point NN. Prove that the lines AL,BM,CNAL,BM,CN are concurrent.
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