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Question
Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Solution
We know that the radius and tangent are perpendicular at their point of contact In right triangle AOP
`AO^2 = OP^2 + PA^2`
⇒ `(6.5) ^2 = (2.5)^2 +PA^2`
⇒`PA^2 = 36`
⇒PA = 6cm
Since, the perpendicular drawn from the center bisects the chord.
∴ PA = PB = 6cm
Now , AB = AP + PB = 6+6 = 12cm
Hence, the length of the chord of the larger circle is 12cm.
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