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Turkey NMO 2000 1st Round - P09 (Geometry)

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July 24, 2012
geometrytrapezoid

Problem Statement

ABCDEABCDE is convex pentagon. m(B^)=m(D^)=90∘m(\widehat{B})=m(\widehat{D})=90^\circ, m(C^)=120∘m(\widehat{C})=120^\circ, ∣AB∣=2|AB|=2, ∣BC∣=∣CD∣=3|BC|=|CD|=\sqrt3, and ∣ED∣=1|ED|=1. ∣AE∣=?|AE|=?
<spanclass=′latex−bold′>(A)</span> 332<spanclass=′latex−bold′>(B)</span> 233<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 3−1<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ \frac{3\sqrt3}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac{2\sqrt3}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac{3}{2} \qquad<span class='latex-bold'>(D)</span>\ \sqrt3 - 1 \qquad<span class='latex-bold'>(E)</span>\ \sqrt3
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