Two concentric circles having radii 17 and 8 | vedclass

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Question

(A) Let the center of the concentric circles be $O$. Let the radius of the larger circle be $R = 17$ and the radius of the smaller circle be $r = 8$.L

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Let the center of the concentric circles be $O$. Let the radius of the larger circle be $R = 17$ and the radius of the smaller circle be $r = 8$.Let $AB$ be the chord of the larger circle that touches the smaller circle at point $P$.Since $AB$ is tangent to the smaller circle at $P$,the radius $OP$ is perpendicular to the chord $AB$ $(OP \perp AB)$.In the right-angled triangle $	riangle OPA$,by the Pythagorean theorem:$OA^2 = OP^2 + AP^2$$17^2 = 8^2 + AP^2$$289 = 64 + AP^2$$AP^2 = 289 - 64 = 225$$AP = \sqrt{225} = 15$.Since the perpendicular from the center to a chord bisects the chord,$AB = 2 	imes AP = 2 	imes 15 = 30$.Therefore,the length of the chord is $30$.

Two concentric circles having radii $17$ and $8$ 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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