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Question

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

Let O be the common center of two concentric circles and let AB be a chord of larger circle touching the smaller circle at P join OP

Since OP is the radius of the smaller circle to any chrod of the circle bisects the chord.

AP=BP

In right ΔAPO we have
OA2=AP2+OP2259=AP2
AP2=16AP=4

Now AB=2,AP=2×4=8[AP=PB]
hence the length of the chord of the larger circle which touches the smaller circle is 8cm.

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