# If the arcs of the same lengths in two circles subtend angles 65°and 110° at the centre, find the ratio of their radii.

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If the arcs of the same lengths in two circles subtend angles 65°and 110° at the centre, find the ratio of their radii.

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Solution: Let r1 and r2 be the radii of the two circles. Given that

Let l be the length of each of the arc. Then l = r1θ1 = r2θ2, which gives

Hence r1 : r2 = 22 : 13.