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Turkey NMO 2000 1st Round - P25 (Geometry)

Source:

July 25, 2012
geometry

Problem Statement

The area of a convex quadrilateral ABCDABCD is 1818. If ∣AB∣+∣BD∣+∣DC∣=12|AB|+|BD|+|DC|=12, then what is ∣AC∣|AC|?
<spanclass=′latex−bold′>(A)</span> 9<spanclass=′latex−bold′>(B)</span> 63<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 62 <span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 6\sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 6\sqrt 2
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