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Turkey NMO 2000 1st Round - P21 (Geometry)

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July 25, 2012
geometrytrigonometrycyclic quadrilateralPythagorean Theorem

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with ∣AB∣=26|AB|=26, ∣BC∣=10|BC|=10, m(ABD^)=45∘m(\widehat{ABD})=45^\circ,m(ACB^)=90∘m(\widehat{ACB})=90^\circ. What is the area of △DAC\triangle DAC ?
<spanclass=′latex−bold′>(A)</span> 120<spanclass=′latex−bold′>(B)</span> 108<spanclass=′latex−bold′>(C)</span> 90<spanclass=′latex−bold′>(D)</span> 84<spanclass=′latex−bold′>(E)</span> 80 <span class='latex-bold'>(A)</span>\ 120 \qquad<span class='latex-bold'>(B)</span>\ 108 \qquad<span class='latex-bold'>(C)</span>\ 90 \qquad<span class='latex-bold'>(D)</span>\ 84 \qquad<span class='latex-bold'>(E)</span>\ 80
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