Two circles are concentric. A central angle forms an arc on both circles. The length of the arc on the smaller circle is 21 in, and the length of the arc on the larger circle is 51 in. If the larger circle has radius 11 in, then what is the radius of the smaller circle?- 4.5 in.- 8.3 in.- 20.4 in.- 16.9 in.

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Given, two circles are concentric.A central angle forms an arc on both circles.The length of the arc on the smaller circle is 21 in, and the length of the arc on the larger circle is 51 in. If the larger circle has radius 11 in, then what is the radius of the smaller circle?Since, arc length s=2πrθ360∘For larger circlearc length s=51in.radius =11inπ=3.14∴51=2(3.14)(11)θ360∘⇒θ=51×s360∘2(3.14)(11)⇒θ=265.78∘Therefore, central angle θ=265.78∘For smaller circlearc length s=21inRadius =?∴21=2(3.14)(r)265.78∘360∘⇒r=21×360∘2(3.14)(265.78∘)⇒r=4.5inAnswer: (a)

Two circles are concentric. A central angle forms an arc on both circles. The length of the arc on t

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