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Example 5 If the arcs of the same lengths in two circles subtend angles 65° and 110° at the center, find the ratio of their radii. We know that 𝑙 = r θ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle 𝑙 = r1 θ = r1 × 65° Converting into radians = r1 × 65° × 𝜋/(180°) = r1 × 𝟏𝟑𝝅/𝟑𝟔 Length of arc of 2nd circle 𝑙 = r2 θ = r2 × 110° Converting into radians = r2 × 110° × 𝜋/(180°) = r2 × 𝟏𝟏𝝅/𝟏𝟖 Given that Length of 1st arc = length of 2nd arc r1 × 𝟏𝟑𝝅/𝟑𝟔 = r2 × 𝟏𝟏𝝅/𝟏𝟖 𝑟1/𝑟2 = 11𝜋/18 × 36/13𝜋 𝑟1/𝑟2 = 22𝜋/13𝜋 𝒓𝟏/𝒓𝟐 = 𝟐𝟐/𝟏𝟑 Hence, r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo