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013

Part of 1962 All Russian Mathematical Olympiad

Problems(1)

ASU 013 All Russian MO 1962 8.1 areas

Source:

6/17/2019
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 A′B′C′D′A'B'C'D' area is five times more than the quadrangle ABCDABCD area.
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