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right angle wanted, AB=BC, circumcircle related (2018 Kyiv City MO Round2 11.2)

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September 14, 2020
circumcirclegeometryright angle

Problem Statement

In the quadrilateral ABCDABCD , AB=BCAB = BC , the point KK is the midpoint of the side CDCD , the rays BKBK and ADAD intersect at the point MM , the circumscribed circle ΔABM \Delta ABM intersects the line ACAC for the second time at the point PP . Prove that ∠BKP=90∘\angle BKP = 90 {} ^ \circ .
(Anton Trygub)
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