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Turkey NMO 2000 1st Round - P05 (Geometry)

Source:

July 24, 2012
geometrytrigonometryparallelogramPythagorean Theoremtrig identitiesLaw of Cosines

Problem Statement

[BD][BD] is a median of ABC\triangle ABC. m(ABD^)=90m(\widehat{ABD})=90^\circ, AB=2|AB|=2, and AC=6|AC|=6. BC=?|BC|=?
<spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 32<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 42<spanclass=latexbold>(E)</span> 26 <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 3\sqrt2 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 4\sqrt2 \qquad<span class='latex-bold'>(E)</span>\ 2\sqrt6