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Last updated at Feb. 17, 2020 by Teachoo
Transcript
Example 5 If the arcs of the same lengths in two circles subtend angles 65ยฐ and 110ยฐ at the center, find the ratio of their radii. We know that ๐ = r ฮธ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle ๐ = r1 ฮธ = r1 ร 65ยฐ = r1 ร 65ยฐ ร ๐/(180ยฐ) = r1 ร 13๐/36 Length of arc of 2nd circle ๐ = r2 ฮธ = r2 ร 110ยฐ = r2 ร 110ยฐ ร ๐/(180ยฐ) = r2 ร 11๐/18 Given that Length of I arc = length of II arc r1 ร 13๐/36 = r2 ร 11๐/18 ๐1/๐2 = 11๐/18 ร 36/13๐ ๐1/๐2 = 22๐/13๐ ๐1/๐2 = 22/13 Hence r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13
Arc length
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