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ratio of areas 5/12 wanted, midpoints related

Source: 2014 Saudi Arabia Pre-TST 1.2

September 12, 2020
geometryratioareas

Problem Statement

Let DD be the midpoint of side BCBC of triangle ABCABC and EE the midpoint of median ADAD. Line BEBE intersects side CACA at FF. Prove that the area of quadrilateral CDEFCDEF is 512\frac{5}{12} the area of triangle ABCABC.
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