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[AEFB] = [DEFC] = 2[AED] = 2[BFC] unit square 2020 BMT Team 8

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January 7, 2022
geometryareassquare

Problem Statement

Let ABCDABCD be a unit square and let EE and FF be points inside ABCDABCD such that the line containing EF‾\overline{EF} is parallel to AB‾\overline{AB}. Point EE is closer to AD‾\overline{AD} than point FF is to AD‾\overline{AD}. The line containing EF‾\overline{EF} also bisects the square into two rectangles of equal area. Suppose [AEFB]=[DEFC]=2[AED]=2[BFC][AEF B] = [DEFC] = 2[AED] = 2[BFC]. The length of segment EF‾\overline{EF} can be expressed as m/nm/n , where m and nn are relatively prime positive integers. Compute m+nm + n.
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