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Question
Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.
Solution
Given that,
Radius of smaller circle = 3 cm
Radius of larger circle = 5 cm
In triangle, OPB
`\implies` (OB)2 = (OP)2 + (BP)2
`\implies` (5)2 = (3)2 + (BP)2
`\implies` (BP)2 = 25 – 9 = 16 = (4)2
`\implies` BP = 4 cm
Also, AP = BP ...(As tangent is bisected at the point of contact)
So, AP = BP = 4 cm
`\implies` AB = 4 + 4 = 8 cm
Length of chord AB = 8 cm.
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