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<ADC = 2<ABE. if <A =<B = 90^o, AB = AD., CD = BC + AD, AD > BC

Source: 2021 Saudi Arabia Training Lists p13 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 5, 2022
geometryanglesequal angles

Problem Statement

Let ABCDABCD be a quadrilateral with ∠A=∠B=90o\angle A = \angle B = 90^o, AB=ADAB = AD. Denote EE as the midpoint of ADAD, suppose that CD=BC+ADCD = BC + AD, AD>BCAD > BC. Prove that ∠ADC=2∠ABE\angle ADC = 2\angle ABE.
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