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ASU 013 All Russian MO 1962 8.1 areas

Source:

June 17, 2019
geometryareas

Problem Statement

Given points A,B,C,D,A' ,B' ,C' ,D', on the extension of the [AB],[BC],[CD],[DA][AB], [BC], [CD], [DA] sides of the convex quadrangle ABCDABCD, such, that the following pairs of vectors are equal: [BB]=[AB],[CC]=[BC],[DD]=[CD],[AA]=[DA].[BB']=[AB], [CC']=[BC], [DD']=[CD], [AA']=[DA]. Prove that the quadrangle ABCDA'B'C'D' area is five times more than the quadrangle ABCDABCD area.