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12 May, 20:15

Suppose that circles R and S have a central angle measuring 60°. Additionally, the length of the intercepted arc for circle R is 10 3 π meters and for circle S is 16 3 π meters.

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  1. 12 May, 20:23
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    15.8 meters

    Step-by-step explanation:

    We have the following information:

    The length of the intercepted arc for the circle R = 103 * π meters

    The arc length of circle S = 163 * π meters

    We also know the radius of the circle R (10) but not that of the circle S (x).

    We are told that circles R and S have a central angle that measures 60 °. Therefore, the radius of circle S to the radius of circle R is equal to the length of the intercepted arc S to the length of the arc R, thus:

    Radius S / Radius R = Length S / Length R

    I know all, except the radius of S, we organize for this value and we have:

    Radius S = (Length S / Length R) * Radius R

    Replacing:

    Radius S = (163 * π / 103 * π) * 10

    Radius S = 15,825 meters

    So the radius of the circle S = 15.8 meters
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