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Points cyclic iff angle is right

Source: RMO Maharashtra and Goa 2016, P4

October 11, 2016
geometry

Problem Statement

Let △ABC\triangle ABC be scalene, with BCBC as the largest side. Let DD be the foot of the perpendicular from AA on side BCBC. Let points K,LK,L be chosen on the lines ABAB and ACAC respectively, such that DD is the midpoint of segment KLKL. Prove that the points B,K,C,LB,K,C,L are concyclic if and only if ∠BAC=90∘\angle BAC=90^{\circ}.
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