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P13 [Geometry] - Turkish NMO 1st Round - 2001

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April 20, 2014
geometrytrigonometry

Problem Statement

Let ABCABC be a triangle such that ∣BC∣=7|BC|=7 and ∣AB∣=9|AB|=9. If m(ABC^)=2m(BCA^)m(\widehat{ABC}) = 2m(\widehat{BCA}), then what is the area of the triangle?
<spanclass=′latex−bold′>(A)</span> 145<spanclass=′latex−bold′>(B)</span> 30<spanclass=′latex−bold′>(C)</span> 106<spanclass=′latex−bold′>(D)</span> 202<spanclass=′latex−bold′>(E)</span> 123 <span class='latex-bold'>(A)</span>\ 14\sqrt 5 \qquad<span class='latex-bold'>(B)</span>\ 30 \qquad<span class='latex-bold'>(C)</span>\ 10\sqrt 6 \qquad<span class='latex-bold'>(D)</span>\ 20 \sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ 12 \sqrt 3
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