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Turkey NMO 2008 1st Round - P29 (Geometry)

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August 27, 2012
geometryparallelograminequalitiesAsymptote

Problem Statement

[AB][AB] and [CD][CD] are not parallel in the convex quadrilateral ABCDABCD. Let EE and FF be the midpoints of [AD][AD] and [BC][BC], respectively. If ∣CD∣=12|CD|=12, ∣AB∣=22|AB|=22, and ∣EF∣=x|EF|=x, what is the sum of integer values of xx?
<spanclass=′latex−bold′>(A)</span> 110<spanclass=′latex−bold′>(B)</span> 114<spanclass=′latex−bold′>(C)</span> 118<spanclass=′latex−bold′>(D)</span> 121<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 110 \qquad<span class='latex-bold'>(B)</span>\ 114 \qquad<span class='latex-bold'>(C)</span>\ 118 \qquad<span class='latex-bold'>(D)</span>\ 121 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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