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Turkey NMO 2007 1st Round - P13 (Geometry)

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October 4, 2012
geometryincentertrigonometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be an circumscribed quadrilateral such that m(A^)=m(B^)=120∘m(\widehat{A})=m(\widehat{B})=120^\circ, m(C^)=30∘m(\widehat{C})=30^\circ, and ∣BC∣=2|BC|=2. What is ∣AD∣|AD|?
<spanclass=′latex−bold′>(A)</span> 3−1<spanclass=′latex−bold′>(B)</span> 2−3<spanclass=′latex−bold′>(C)</span> 6−2<spanclass=′latex−bold′>(D)</span> 2−2<spanclass=′latex−bold′>(E)</span> 3−3 <span class='latex-bold'>(A)</span>\ \sqrt 3 - 1 \qquad<span class='latex-bold'>(B)</span>\ \sqrt 2 - 3 \qquad<span class='latex-bold'>(C)</span>\ \sqrt 6 - \sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ 2 - \sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ 3 - \sqrt 3
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