odot(O, 17) and odot(O, 15) are concentric ci | vedclass

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(C) Let $O$ be the common center of the two concentric circles.Let $R = 17$ be the radius of the outer circle and $r = 15$ be the radius of the inner

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) Let $O$ be the common center of the two concentric circles.Let $R = 17$ be the radius of the outer circle and $r = 15$ be the radius of the inner circle.The chord $\overline{AB}$ of the outer circle is tangent to the inner circle at point $M$.Since the radius is perpendicular to the tangent at the point of contact,$OM \perp AB$.In $	riangle OMA$,by the Pythagorean theorem: $OA^2 = OM^2 + AM^2$.Substituting the values: $17^2 = 15^2 + AM^2$.$289 = 225 + AM^2$.$AM^2 = 289 - 225 = 64$.$AM = \sqrt{64} = 8$.Since the perpendicular from the center to a chord bisects the chord,$AB = 2 	imes AM$.$AB = 2 	imes 8 = 16$.

$\odot(O, 17)$ and $\odot(O, 15)$ are concentric circles. The chord $\overline{AB}$ of $\odot(O, 17)$ touches $\odot(O, 15)$. Then $AB = \ldots$

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