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Question

If radii of two consecutive circles are 15cm and 17cm then find the length of one circle which is tangent to one other

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Solution


O is the centre of both circles. Chord AB of larger circle touches smaller circle at P. Radius OP perpendicular chord AB.
Radius OA = 15 cm and radius OP = 15cm.
Applying Puthagoras theorem to triangleAOP, A P squared equals O A squared minus O P squared equals space 17 squared minus 15 squared space equals 289 minus 225 equals 64
=> AP =8. Radius perpendicular to a chord bisects it so AP = 1/2 AB
AB = 2PB = 16cm
Answer: Length of chord = 16cm

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