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collinear wanted, arc midpoint related

Source: 2015 Saudi Arabia IMO TST III p2

July 24, 2020
geometryarc midpointcollinear

Problem Statement

Let ABCABC be a triangle and ω\omega its circumcircle. Point DD lies on the arc BCBC (not containing AA) of ω\omega and is different from B,CB, C and the midpoint of arc BCBC . The tangent line to ω\omega at DD intersects lines BC,CA,ABBC, CA,AB at A′,B′,C′A', B',C' respectively. Lines BB′BB' and CC′CC' intersect at EE. Line AA′AA' intersects again circle ω\omega at FF. Prove that the three points D,E,FD,E,F are colinear.
Malik Talbi
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