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Some geometry

Source: St Petersburg Olympiad 2011, Grade 11, P2

September 15, 2017
geometrycircumcircle

Problem Statement

ABCABC-triangle with circumcenter OO and ∠B=30\angle B=30. BOBO intersect ACAC at KK. LL - midpoint of arc OCOC of circumcircle KOCKOC, that does not contains KK. Prove, that A,B,L,KA,B,L,K are concyclic.
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