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AK = KL inside a cyclic pentagon ABCDE with AB = BC = CD

Source: Czech-Polish-Slovak Junior Match 2013, Individual p3 CPSJ

March 14, 2020
equal segmentsgeometrypentagonCyclic

Problem Statement

The ABCDEABCDE pentagon is inscribed in a circle and AB=BC=CDAB = BC = CD. Segments ACAC and BEBE intersect at KK, and Segments ADAD and CECE intersect at pointL L. Prove that AK=KLAK = KL.
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