MathDB
Two Circles and a Hexagon

Source: 2010 AMC 10B Problem 20

February 26, 2010
ratiogeometryAMC

Problem Statement

Two circles lie outside regular hexagon ABCDEF ABCDEF. The first is tangent to AB \overline{AB}, and the second is tangent to DE \overline{DE}. Both are tangent to lines BC BC and FA FA. What is the ratio of the area of the second circle to that of the first circle? <spanclass=latexbold>(A)</span> 18<spanclass=latexbold>(B)</span> 27<spanclass=latexbold>(C)</span> 36<spanclass=latexbold>(D)</span> 81<spanclass=latexbold>(E)</span> 108 <span class='latex-bold'>(A)</span>\ 18\qquad<span class='latex-bold'>(B)</span>\ 27\qquad<span class='latex-bold'>(C)</span>\ 36\qquad<span class='latex-bold'>(D)</span>\ 81\qquad<span class='latex-bold'>(E)</span>\ 108