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Four Points in a Plane

Source: 2012 AMC 10B Problem #21

February 23, 2012
ratioinequalitiestriangle inequalityAMC

Problem Statement

Four distinct points are arranged in a plane so that the segments connecting them has lengths a,a,a,a,2a,a,a,a,a,2a, and bb. What is the ratio of bb to aa?
<spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> π <span class='latex-bold'>(A)</span>\ \sqrt{3}\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ \sqrt{5}\qquad<span class='latex-bold'>(D)</span>\ 3\qquad<span class='latex-bold'>(E)</span>\ \pi