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2017 Geometry #8

Source:

November 19, 2022
2017Geometry Test

Problem Statement

Let △ABC\triangle ABC be a right triangle with right angle ∠ACB\angle ACB. Square DEFGDEFG is contained inside triangle ABCABC such that DD lies on ABAB, EE lies on BCBC, FF lies on ACAC, AD=AFAD=AF, and GA=GD=GFGA=GD=GF. Suppose that CE=2CE=2. If MM is the area of triangle ABCABC and NN is the area of square DEFGDEFG, compute M−NM-N.
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