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Externally Tangent Circles

Source: 2012 AMC10A Problem #11

February 8, 2012
analytic geometrygraphing linesslopeAMC

Problem Statement

Externally tangent circles with centers at points AA and BB have radii of lengths 55 and 33, respectively. A line externally tangent to both circles intersects ray ABAB at point CC. What is BCBC?
<spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 4.8<spanclass=latexbold>(C)</span> 10.2<spanclass=latexbold>(D)</span> 12<spanclass=latexbold>(E)</span> 14.4 <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 4.8 \qquad<span class='latex-bold'>(C)</span>\ 10.2 \qquad<span class='latex-bold'>(D)</span>\ 12 \qquad<span class='latex-bold'>(E)</span>\ 14.4