Two concentric circles having radii 5 and 13 | vedclass

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Question

(C) Let $O$ be the common center of the two concentric circles.Let $AB$ be the chord of the larger circle which touches the smaller circle at point $M

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) Let $O$ be the common center of the two concentric circles.Let $AB$ be the chord of the larger circle which touches the smaller circle at point $M$.$OM$ is the radius of the smaller circle,so $OM = 5$.$OB$ is the radius of the larger circle,so $OB = 13$.Since the radius is perpendicular to the tangent at the point of contact,$\angle OMB = 90^{\circ}$.In right-angled $\Delta OMB$,by Pythagoras theorem:$OB^2 = OM^2 + MB^2$$13^2 = 5^2 + MB^2$$169 = 25 + MB^2$$MB^2 = 169 - 25 = 144$$MB = \sqrt{144} = 12$.The perpendicular from the center to a chord bisects the chord.Therefore,$AB = 2 	imes MB = 2 	imes 12 = 24$.

Two concentric circles having radii $5$ and $13$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Then the length of the chord is $\ldots \ldots \ldots \ldots.$

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