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Three circles of radius 9 cm are kept touching each other. The string is tightly tied around the three circles. What is the length (in cm) of the string?

Three circles of radius 9 cm are kept touching each other. The string is tightly tied around the three circles. What is the length (in cm) of the string? Correct Answer 54 + 18π

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The length of the string not in contact with circle = 2r + 2r + 2r = 6r = 6 × 9 = 54.

By symmetry, the angles swiped by string on one circle is 120.

⇒ Length of string touching circle = 2πr/3 + 2πr/3 + 2πr/3 = 2πr = 2 × 9 × π = 18π

Total length = 54 + 18π.

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