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Turkish NMO First Round - 2012 Problem - 29 {Geometry}

Source:

July 1, 2012
geometrytrigonometrytrig identitiesLaw of Sines

Problem Statement

Let DD and EE be points on [BC][BC] and [AC][AC] of acute ABC\triangle ABC, respectively. ADAD and BEBE meet at FF. If AF=CD=2BF=2CE|AF|=|CD|=2|BF|=2|CE|, and Area(ABF)=Area(DEC)Area(\triangle ABF) = Area(\triangle DEC), then Area(AFC)/Area(BFC)=?Area(\triangle AFC)/Area(\triangle BFC) = ?
<spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 22<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 2<spanclass=latexbold>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 4 \qquad <span class='latex-bold'>(B)</span>\ 2\sqrt2 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ \sqrt2 \qquad <span class='latex-bold'>(E)</span>\ 1