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P13 [Geometry] - Turkish NMO 1st Round - 2003

Source:

December 10, 2013
geometryangle bisector

Problem Statement

Let ABCABC be a triangle such that ∣AB∣=8|AB|=8 and ∣AC∣=2∣BC∣|AC|=2|BC|. What is the largest value of altitude from side [AB][AB]?
<spanclass=′latex−bold′>(A)</span> 32<spanclass=′latex−bold′>(B)</span> 33<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 163<spanclass=′latex−bold′>(E)</span> 6 <span class='latex-bold'>(A)</span>\ 3\sqrt 2 \qquad<span class='latex-bold'>(B)</span>\ 3\sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ \dfrac {16}3 \qquad<span class='latex-bold'>(E)</span>\ 6
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