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P17 [Geometry] - Turkish NMO 1st Round - 2005

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October 26, 2013
geometrytrigonometry

Problem Statement

Construct outer squares ABMNABMN, BCKLBCKL, ACPQACPQ on sides [AB][AB], [BC][BC], [CA][CA] of triangle ABCABC, respectively. Construct squares NQZTNQZT and KPYXKPYX on segments [NQ][NQ] and [KP][KP]. If Area(ABMN)−Area(BCKL)=1Area(ABMN) - Area(BCKL)=1, what is Area(NQZT)−Area(KPYX)Area(NQZT)-Area(KPYX)?
<spanclass=′latex−bold′>(A)</span> 34<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 4 <span class='latex-bold'>(A)</span>\ \dfrac 34 \qquad<span class='latex-bold'>(B)</span>\ \dfrac 53 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4
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