MathDB
Lines and Circles

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February 7, 2009
geometrysimilar triangles

Problem Statement

The straight line AB‾ \overline{AB} is divided at C C so that AC\equal{}3CB. Circles are described on AC‾ \overline{AC} and CB‾ \overline{CB} as diameters and a common tangent meets AB AB produced at D D. Then BD BD equals: <spanclass=′latex−bold′>(A)</span> diameter of the smaller circle<spanclass=′latex−bold′>(B)</span> radius of the smaller circle<spanclass=′latex−bold′>(C)</span> radius of the larger circle<spanclass=′latex−bold′>(D)</span> CB3<spanclass=′latex−bold′>(E)</span> the difference of the two radii <span class='latex-bold'>(A)</span>\ \text{diameter of the smaller circle} \\ <span class='latex-bold'>(B)</span>\ \text{radius of the smaller circle} \\ <span class='latex-bold'>(C)</span>\ \text{radius of the larger circle} \\ <span class='latex-bold'>(D)</span>\ CB\sqrt{3}\\ <span class='latex-bold'>(E)</span>\ \text{the difference of the two radii}
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