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Junior Regional Olympiad - FBH 2016 Grade 7 Problem 4

Source:

September 29, 2018
geometry

Problem Statement

In right angled triangle ABCABC point DD is midpoint of hypotenuse, and EE and FF are points on shorter sides ACAC and BCBC, respectively, such that DE⊥DFDE \perp DF. Prove that EF2=AE2+BF2EF^2=AE^2+BF^2
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