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P05 [Geometry] - Turkish NMO 1st Round - 2001

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April 18, 2014
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezoid such that AB∥CDAB \parallel CD, ∣AB∣<∣CD∣|AB|<|CD|, and Area(ABC)=30\text{Area}(ABC)=30. Let the line through BB parallel to ADAD meet [AC][AC] at EE. If ∣AE∣:∣EC∣=3:2|AE|:|EC|=3:2, then what is the area of trapezoid ABCDABCD?
<spanclass=′latex−bold′>(A)</span> 45<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 72<spanclass=′latex−bold′>(D)</span> 80<spanclass=′latex−bold′>(E)</span> 90 <span class='latex-bold'>(A)</span>\ 45 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 72 \qquad<span class='latex-bold'>(D)</span>\ 80 \qquad<span class='latex-bold'>(E)</span>\ 90
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