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Ratios of Various Lengths on Triangle

Source:

January 12, 2009
ratiogeometrysimilar triangles

Problem Statement

Point E E is selected on side AB AB of triangle ABC ABC in such a way that AE: EB \equal{} 1: 3 and point D D is selected on side BC BC such that CD: DB \equal{} 1: 2. The point of intersection of AD AD and CE CE is F F. Then \frac {EF}{FC} \plus{} \frac {AF}{FD} is: <spanclass=latexbold>(A)</span> 45<spanclass=latexbold>(B)</span> 54<spanclass=latexbold>(C)</span> 32<spanclass=latexbold>(D)</span> 2<spanclass=latexbold>(E)</span> 52 <span class='latex-bold'>(A)</span>\ \frac {4}{5} \qquad <span class='latex-bold'>(B)</span>\ \frac {5}{4} \qquad <span class='latex-bold'>(C)</span>\ \frac {3}{2} \qquad <span class='latex-bold'>(D)</span>\ 2 \qquad <span class='latex-bold'>(E)</span>\ \frac {5}{2}