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Turkey NMO 2006 1st Round - P17 (Geometry)

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February 2, 2013
geometrytrigonometry

Problem Statement

Let DD be a point on the side [BC][BC] of △ABC\triangle ABC such that ∣BD∣=2|BD|=2 and ∣DC∣=6|DC|=6. If ∣AB∣=4|AB|=4 and m(ACB^)=20∘m(\widehat{ACB})=20^\circ, then what is m(BAD^)m(\widehat {BAD})?
<spanclass=′latex−bold′>(A)</span> 10∘<spanclass=′latex−bold′>(B)</span> 18∘<spanclass=′latex−bold′>(C)</span> 20∘<spanclass=′latex−bold′>(D)</span> 22∘<spanclass=′latex−bold′>(E)</span> 25∘ <span class='latex-bold'>(A)</span>\ 10^\circ \qquad<span class='latex-bold'>(B)</span>\ 18^\circ \qquad<span class='latex-bold'>(C)</span>\ 20^\circ \qquad<span class='latex-bold'>(D)</span>\ 22^\circ \qquad<span class='latex-bold'>(E)</span>\ 25^\circ
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