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AB = BC + AD in convex ABCD with many data given

Source: IGO Elementary 2016 5

July 22, 2018
geometryanglesquadrilateral

Problem Statement

Let ABCDABCD be a convex quadrilateral with these properties: ∠ADC=135o\angle ADC = 135^o and ∠ADB−∠ABD=2∠DAB=4∠CBD\angle ADB - \angle ABD = 2\angle DAB = 4\angle CBD. If BC=2CDBC = \sqrt2 CD , prove that AB=BC+ADAB = BC + AD.
by Mahdi Etesami Fard
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