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angle chasing inside a square ABCD, ML = KL given

Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p5

August 16, 2020
squareanglesequal segments

Problem Statement

Points KK and MM are taken on the sides ABAB and CDCD of square ABCDABCD, respectively, and on the diagonal ACAC - point LL such that ML=KLML = KL. Let PP be the intersection point of the segments MKMK and BDBD. Find the angle KPL\angle KPL.