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Turkey NMO 2007 1st Round - P21 (Geometry)

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October 5, 2012
geometry

Problem Statement

Let ABCDABCD be a quadrilateral such that m(A^)=m(D^)=90∘m(\widehat{A}) = m(\widehat{D}) = 90^\circ. Let MM be the midpoint of [DC][DC]. If AC⊥BMAC\perp BM, ∣DC∣=12|DC|=12, and ∣AB∣=9|AB|=9, then what is ∣AD∣|AD|?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 9<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 9 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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