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P25 [Geometry] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014
geometrycircumcircletrigonometry

Problem Statement

The circumradius of acute triangle ABCABC is twice of the distance of its circumcenter to ABAB. If ∣AC∣=2|AC|=2 and ∣BC∣=3|BC|=3, what is the altitude passing through CC?
<spanclass=′latex−bold′>(A)</span> 14<spanclass=′latex−bold′>(B)</span> 3721<spanclass=′latex−bold′>(C)</span> 4721<spanclass=′latex−bold′>(D)</span> 1221<spanclass=′latex−bold′>(E)</span> 2314 <span class='latex-bold'>(A)</span>\ \sqrt {14} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{3}{7}\sqrt{21} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{4}{7}\sqrt{21} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{1}{2}\sqrt{21} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{2}{3}\sqrt{14}
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