Two different circles ω1 ,ω2, with centers O1,O2 respectively intersect at the points A,B. The line O1B intersects ω2 at the point F(F=B), and the line O2B intersects ω1 at the point E(E=B). A line was drawn through the point B, parallel to the EF, which intersects ω1 at the point M(M=B), and ω2 at the point N(N=B). Prove that the lines ME,AB and NF intersect at one point. geometrycirclesconcurrencyconcurrentChampions Tournament