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collinear points, starting with the circumcircle

Source: BMO Shortlist 2015 G2 (Saudi Arabia)

September 27, 2018
geometrycircumcirclecollinear

Problem Statement

Let ABCABC be a triangle with circumcircle ω\omega . Point DD lies on the arc BCBC of ω\omega and is different than B,CB,C and the midpoint of arc BCBC. Tangent of Γ\Gamma at DD intersects lines BCBC, CACA, ABAB at A′,B′,C′A',B',C', respectively. Lines BB′BB' and CC′CC' intersect at EE. Line AA′AA' intersects the circle ω\omega again at FF. Prove that points D,E,FD,E,F are collinear.
(Saudi Arabia)
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