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60 deg strikes again

Source: LMAO 2024 P4

June 1, 2024
geometrylmaoLMAO Mock

Problem Statement

Let ABCABC be a triangle with circumcenter OO and ∠BAC=60∘\angle BAC = 60^{\circ}. The internal angle bisector of ∠BAC\angle BAC meets line BCBC and the circumcircle of △ABC\triangle ABC in points M,LM,L respectively. Let KK denote the reflection of BL∩ACBL\cap AC over the line BCBC. Let DD be on the line COCO with DMDM perpendicular to KLKL. Prove that points K,A,DK,A,D are collinear.
Proposed by Sanjana Philo Chacko
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