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Convex Quadrilateral

Source: Indonesia Mathematics Olympiad 2005 Day 2 Problem 7

June 2, 2008
geometrygeometry proposed

Problem Statement

Let ABCD ABCD be a convex quadrilateral. Square AB1A2B AB_1A_2B is constructed such that the two vertices A2,B1 A_2,B_1 is located outside ABCD ABCD. Similarly, we construct squares BC1B2C BC_1B_2C, CD1C2D CD_1C_2D, DA1D2A DA_1D_2A. Let K K be the intersection of AA2 AA_2 and BB1 BB_1, L L be the intersection of BB2 BB_2 and CC1 CC_1, M M be the intersection of CC2 CC_2 and DD1 DD_1, and N N be the intersection of DD2 DD_2 and AA1 AA_1. Prove that KM KM is perpendicular to LN LN.
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