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Question

If arcs of same length in two circles subtend angles of 60 and 75 at their center, find the ratios of their radii.

A
r1:r2=5:4
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B
r1:r2=4:5
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C
r1:r2=5:3
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D
r1:r2=3:5
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Solution

The correct option is A r1:r2=5:4
Let r1 and r2 be the radii of the given circles and let their arcs be of same length s subtending angles of 60 and 75 at their centers. Now,
60 = (60×π180)R = (π3)R and 750=(75×π180)R=(5π12)R
π3=sr1 and 5π12=sr2
π3r1=s and 5π12r2=s
π3r1=5π12r2
4r1=5r2
r1:r2=5:4

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