MathDB
P01 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 21, 2014
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral such that m(DAB^)=m(CBD^)=120∘m \left (\widehat{DAB} \right )=m \left (\widehat{CBD} \right )=120^{\circ}, ∣AB∣=2|AB|=2, ∣AD∣=4|AD|=4 and ∣BC∣=∣BD∣|BC|=|BD|. If the line through CC which is parallel to ABAB meets ADAD at EE, what is ∣CE∣|CE|?
<spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 7 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
Back to ProblemsView on AoPS