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Turkey NMO 2007 1st Round - P09 (Geometry)

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October 4, 2012
geometrytrigonometry

Problem Statement

Let ∣AB∣=3|AB|=3 and the length of the altitude from CC be 22 in △ABC\triangle ABC. What is the maximum value of the product of the lengths of the other two altitudes?
<spanclass=′latex−bold′>(A)</span> 14425<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ \frac{144}{25} \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ 3\sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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