MathDB

9

Part of 2005 National Olympiad First Round

Problems(1)

P09 [Geometry] - Turkish NMO 1st Round - 2005

Source:

10/26/2013
Let ABCABC be a triangle with circumradius 11. If the center of the circle passing through AA, CC, and the orthocenter of △ABC\triangle ABC lies on the circumcircle of △ABC\triangle ABC, what is ∣AC∣|AC|?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 32 \qquad<span class='latex-bold'>(D)</span>\ \sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ \sqrt 3
geometrycircumcircletrigonometry