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Turkey NMO 2006 1st Round - P09 (Geometry)

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February 2, 2013
geometryangle bisector

Problem Statement

ABCABC is a triangle with ∣AB∣=6|AB|=6, ∣BC∣=7|BC|=7, and ∣AC∣=8|AC|=8. Let the angle bisector of ∠A\angle A intersect BCBC at DD. If EE is a point on [AC][AC] such that ∣CE∣=2|CE|=2, what is ∣DE∣|DE|?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 175<spanclass=′latex−bold′>(C)</span> 72<spanclass=′latex−bold′>(D)</span> 23<spanclass=′latex−bold′>(E)</span> 32 <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ \frac {17}5 \qquad<span class='latex-bold'>(C)</span>\ \frac 72 \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt 3 \qquad<span class='latex-bold'>(E)</span>\ 3\sqrt 2
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