MathDB

29

Part of 2012 National Olympiad First Round

Problems(1)

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

Source:

7/1/2012
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∣=2∣BF∣=2∣CE∣|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=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 22<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(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
geometrytrigonometrytrig identitiesLaw of Sines