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(DEF) <=\frac{EF^2}{4 AD^2} if AFDE is cyclic and (ABC)=1

Source: Mathcenter Contest / Oly - Thai Forum 2008 R1 p7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 10, 2022
geometryarea of a triangleareasgeometric inequality

Problem Statement

ABCABC is a triangle with an area of 11 square meter. Given the point DD on BCBC, point EE on CACA, point FF on ABAB, such that quadrilateral AFDEAFDE is cyclic. Prove that the area of DEF≤EF24AD2DEF \le \frac{EF^2}{4 AD^2}.
(holmes)
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