Two concentric circles having radii 41 and 40 | vedclass

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(B) Let the radii of the two concentric circles be $R = 41$ and $r = 40$. Let $O$ be the common center. Let $AB$ be the chord of the larger circle tha

Vedclass · Accepted Answer

$18$

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(B) Let the radii of the two concentric circles be $R = 41$ and $r = 40$. Let $O$ be the common center. Let $AB$ be the chord of the larger circle that touches the smaller circle at point $P$. Since the chord touches the smaller circle,$OP$ is perpendicular to $AB$ and $OP = r = 40$. In the right-angled triangle $	riangle OPA$,by the Pythagorean theorem: $OA^2 = OP^2 + AP^2$ $41^2 = 40^2 + AP^2$ $1681 = 1600 + AP^2$ $AP^2 = 1681 - 1600 = 81$ $AP = 9$. Since the perpendicular from the center to a chord bisects the chord,the length of the chord $AB = 2 	imes AP = 2 	imes 9 = 18$.

Two concentric circles having radii $41$ and $40$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

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