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P05 [Geometry] - Turkish NMO 1st Round - 2003

Source:

May 9, 2014
geometrytrigonometry

Problem Statement

Let ABCABC be a triangle and DD be the foot of the altitude from CC to ABAB. If ∣CH∣=∣HD∣|CH|=|HD| where HH is the orthocenter, what is tan⁡A^⋅tan⁡B^\tan \widehat {A} \cdot \tan \widehat{B}?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3/2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ \sqrt 2 \qquad<span class='latex-bold'>(C)</span>\ 3/2 \qquad<span class='latex-bold'>(D)</span>\ \sqrt 3 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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