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Example 5 - If arcs of same lengths in two circles subtend - Examples

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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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 There are 2 circle of different radius So the radius be denoted by r1 and r2 Length of arc of Ist circle 𝑙 = r1 θ = r1 × 65o = r1 × 65o × 𝜋/(180°) = r1 × (13 𝜋)/36 It is give that Arcs are of same length Hence Length of I arc = length of II arc r1 × (13 𝜋)/36 = r2 × (11 𝜋)/18 𝑟1/𝑟2 = (11 𝜋)/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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