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Cyclic trapezoid

Source: 239 2012 S5

July 30, 2020
geometrytrapezoid

Problem Statement

Point MM is the midpoint of the base ADAD of trapezoid ABCDABCD inscribed in circle SS. Rays ABAB and DCDC intersect at point PP, and ray BMBM intersects SS at point KK. The circumscribed circle of triangle PBKPBK intersects line BCBC at point LL. Prove that ∠LDP=90∘\angle{LDP} = 90^{\circ}.
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