All the arcs in the following diagram are semi-circles. This diagram shows two paths connecting A to B. Path 1 is the single large semi-circle and Path 2 consists of the chain of small semi-circles. Then
A
Path 1 is longer than Path 2
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B
Path 1 is of the same length as Path 2
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C
Path 1 is shorter than Path 2
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D
Path 1 is of the same length as Path 2, only if the number of semi-circles is not more than 4.
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Solution
The correct option is A Path 1 is of the same length as Path 2 Let there are n small semi-circles in the chain of small semicircles with radius r. ∴ Length of single large semi-circle =12(2πnr)=nπr Path 1=nπr Length of small circles =n×12(2πr)=nπr Path 2=nπr So paths 1 and 2 will always be equal.