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 65Β°and 110Β° at the center, find the ratio of their radii. We know that 𝑙 = r ΞΈ There are 2 circle of different radius So the radius be denoted by r1 and r2 Length of arc of Ist circle 𝑙 = r1 ΞΈ = r1 Γ— 65o = r1 Γ— 65o Γ— πœ‹/(180Β°) = r1 Γ— (13 πœ‹)/36 It is give that Arcs are of same length Hence Length of I arc = length of II arc r1 Γ— (13 πœ‹)/36 = r2 Γ— (11 πœ‹)/18 π‘Ÿ1/π‘Ÿ2 = (11 πœ‹)/18 Γ— 36/13πœ‹ π‘Ÿ1/π‘Ÿ2 = 22πœ‹/13πœ‹ π‘Ÿ1/π‘Ÿ2 = 22/13 Hence r1 : r2 = 22 : 13 So Ratio of Radius = 22 : 13

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