MathDB
P01 [Geometry] - Turkish NMO 1st Round - 2005

Source:

October 26, 2013
geometry

Problem Statement

The circle with radius 44 passing through AA and BB is tangent to the circle with radius 33 passing through AA and CC, where ∣AB∣=2|AB|=2. If the line BCBC is tangent to the second circle, what is ∣BC∣|BC|?
<spanclass=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 2+432<spanclass=′latex−bold′>(C)</span> 52<spanclass=′latex−bold′>(D)</span> 4+9<spanclass=′latex−bold′>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 2 + \dfrac{\sqrt{43}}2 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 52 \qquad<span class='latex-bold'>(D)</span>\ 4 + \sqrt 9 \qquad<span class='latex-bold'>(E)</span>\ \sqrt 7
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