Let ABC be a triangle with circumcircle ω . Point D lies on the arc BC of ω and is different than B,C and the midpoint of arc BC. Tangent of Γ at D intersects lines BC, CA, AB at A′,B′,C′, respectively. Lines BB′ and CC′ intersect at E. Line AA′ intersects the circle ω again at F. Prove that points D,E,F are collinear.(Saudi Arabia) geometrycircumcirclecollinear