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PK = LQ wanted, 2 equilateral triangles outside convex cyclic ABCD

Source: 2004 Oral Moscow Geometry Olympiad grade 9 p5

October 27, 2020
geometryequal segmentscyclic quadrilateral

Problem Statement

The diagonals of the inscribed quadrilateral ABCDABCD meet at the point MM, ∠AMB=60o\angle AMB = 60^o. Equilateral triangles ADKADK and BCLBCL are built outward on sides ADAD and BCBC. Line KLKL meets the circle circumscribed ariound ABCDABCD at points PP and QQ. Prove that PK=LQPK = LQ.
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