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Special quadrilateral

Source: own, Iran MO 3rd round 2019 mid-terms - Geometry P1

July 31, 2019
geometrycyclic quadrilateral

Problem Statement

Given a cyclic quadrilateral ABCDABCD. There is a point PP on side BCBC such that ∠PAB=∠PDC=90∘\angle PAB=\angle PDC=90^\circ. The medians of vertexes AA and DD in triangles PABPAB and PDCPDC meet at KK and the bisectors of ∠PAB\angle PAB and ∠PDC\angle PDC meet at LL. Prove that KL⊥BCKL\perp BC.
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