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P09 [Geometry] - Turkish NMO 1st Round - 2014

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May 22, 2014
geometry

Problem Statement

Let DD be a point on side [BC][BC] of △ABC\triangle ABC such that ∣AB∣=3,∣CD∣=1|AB|=3, |CD|=1 and ∣AC∣=∣BD∣=5|AC|=|BD|=\sqrt{5}. If the BB-altitude of △ABC\triangle ABC meets ADAD at EE, what is ∣CE∣|CE|?
<spanclass=′latex−bold′>(A)</span> 25<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 23<spanclass=′latex−bold′>(D)</span> 52<spanclass=′latex−bold′>(E)</span> 32 <span class='latex-bold'>(A)</span>\ \dfrac{2}{\sqrt{5}} \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ \dfrac{2}{\sqrt{3}} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{\sqrt{5}}{2} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{3}{2}
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