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Turkish NMO First Round - 1999 P-01 (Geometry)

Source:

July 3, 2012
geometry

Problem Statement

Let ABC ABC be a triangle with \left|AB\right| \equal{} 14, \left|BC\right| \equal{} 12, \left|AC\right| \equal{} 10. Let D D be a point on [AC] \left[AC\right] and E E be a point on [BC] \left[BC\right] such that \left|AD\right| \equal{} 4 and Area\left(ABC\right) \equal{} 2Area\left(CDE\right). Find Area(ABE) Area\left(ABE\right).
<spanclass=′latex−bold′>(A)</span> 46<spanclass=′latex−bold′>(B)</span> 62<spanclass=′latex−bold′>(C)</span> 36<spanclass=′latex−bold′>(D)</span> 42<spanclass=′latex−bold′>(E)</span> 45<span class='latex-bold'>(A)</span>\ 4\sqrt {6} \qquad<span class='latex-bold'>(B)</span>\ 6\sqrt {2} \qquad<span class='latex-bold'>(C)</span>\ 3\sqrt {6} \qquad<span class='latex-bold'>(D)</span>\ 4\sqrt {2} \qquad<span class='latex-bold'>(E)</span>\ 4\sqrt {5}
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