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equilateral ABP wanted, AD = BC, <A + <B = 120^o, DCP equilateral given

Source: Moldova JBMO TST 2001 1.3

July 9, 2020
geometryEquilateralequal segments

Problem Statement

Let the convex quadrilateral ABCDABCD with AD=BCAD = BC ¸and ∠A+∠B=120o\angle A + \angle B = 120^o. Take a point PP in the plane so that the line CDCD separates the points AA and PP, and the DCPDCP triangle is equilateral. Show that the triangle ABPABP is equilateral. It is the true statement for a non-convex quadrilateral?
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