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Common Chord to two Circles

Source: 2014 AMC 12A #12

February 5, 2014
ratiogeometrytrigonometryLaTeXAMC 10trig identitiesLaw of Cosines

Problem Statement

Two circles intersect at points AA and BB. The minor arcs ABAB measure 30∘30^\circ on one circle and 60∘60^\circ on the other circle. What is the ratio of the area of the larger circle to the area of the smaller circle?
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>1+3<spanclass=′latex−bold′>(C)</span>3<spanclass=′latex−bold′>(D)</span>2+3<spanclass=′latex−bold′>(E)</span>4<span class='latex-bold'>(A) </span>2\qquad <span class='latex-bold'>(B) </span>1+\sqrt3\qquad <span class='latex-bold'>(C) </span>3\qquad <span class='latex-bold'>(D) </span>2+\sqrt3\qquad <span class='latex-bold'>(E) </span>4\qquad
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