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2016 preRMO p4, <C=90^o, AD = DE = EF = FB, CD^2 +CE^2 +CF^2 = 350

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August 9, 2019
geometryright triangle

Problem Statement

Consider a right-angled triangle ABCABC with ∠C=90o\angle C = 90^o. Suppose that the hypotenuse ABAB is divided into four equal parts by the points D,E,FD,E,F, such that AD=DE=EF=FBAD = DE = EF = FB. If CD2+CE2+CF2=350CD^2 +CE^2 +CF^2 = 350, find the length of ABAB.
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