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<DEF = 90^o wanted, EF = DE in square ABCE (2021 Polish JMO R2 p2)

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April 8, 2021
geometryright anglesquare

Problem Statement

Given is the square ABCDABCD. Point EE lies on the diagonal ACAC, where AE>ECAE> EC. On the side ABAB, a different point from BB has been selected for which EF=DEEF = DE. Prove that DEF=90o\angle DEF = 90^o.