Two concentric circles are of radii 5 , cm an | vedclass

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Question

(C) Let the two concentric circles be centered at point $O$. Let $PQ$ be the chord of the larger circle which touches the smaller circle at point $A$.

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) Let the two concentric circles be centered at point $O$. Let $PQ$ be the chord of the larger circle which touches the smaller circle at point $A$. Therefore,$PQ$ is tangent to the smaller circle at point $A$.Since $OA$ is the radius of the smaller circle and $PQ$ is the tangent,$OA \perp PQ$.Applying the Pythagoras theorem in $	riangle OAP$,we have:$OA^2 + AP^2 = OP^2$$3^2 + AP^2 = 5^2$$9 + AP^2 = 25$$AP^2 = 25 - 9 = 16$$AP = \sqrt{16} = 4 \, cm$.Since the perpendicular from the center of a circle to a chord bisects the chord,we have $AP = AQ$.Therefore,the length of the chord $PQ = AP + AQ = 2 	imes AP = 2 	imes 4 = 8 \, cm$.

Two concentric circles are of radii $5 \, cm$ and $3 \, cm$. Find the length of the chord of the larger circle which touches the smaller circle.

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