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Turkey NMO 2010 1st Round - P05 (Geometry)

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July 26, 2012
geometrytrigonometry

Problem Statement

Let ABCDABCD be a convex quadrilateral such that ∣AB∣=10|AB|=10, ∣CD∣=36|CD|=3\sqrt 6, m(ABD^)=60∘m(\widehat{ABD})=60^\circ, m(BDC^)=45∘m(\widehat{BDC})=45^\circ, and ∣BD∣=13+33|BD|=13+3\sqrt 3. What is ∣AC∣|AC| ?
<spanclass=′latex−bold′>(A)</span> 20<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 20 \qquad<span class='latex-bold'>(B)</span>\ 18 \qquad<span class='latex-bold'>(C)</span>\ 16 \qquad<span class='latex-bold'>(D)</span>\ 14 \qquad<span class='latex-bold'>(E)</span>\ 12
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