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Square, circle, and areas

Source: 2013 SDMO Middle School Problem 3

August 25, 2016
ratiogeometry

Problem Statement

Let ABCDABCD be a square, and let Γ\Gamma be the circle that is inscribed in square ABCDABCD. Let EE and FF be points on line segments ABAB and ADAD, respectively, so that EFEF is tangent to Γ\Gamma. Find the ratio of the area of triangle CEFCEF to the area of square ABCDABCD.
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