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

Example 5 - Chapter 3 Class 11 Trigonometric Functions - Part 2
Example 5 - Chapter 3 Class 11 Trigonometric Functions - Part 3

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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 Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle 𝑙 = r1 ΞΈ = r1 Γ— 65Β° = r1 Γ— 65Β° Γ— πœ‹/(180Β°) = r1 Γ— 13πœ‹/36 Length of arc of 2nd circle 𝑙 = r2 ΞΈ = r2 Γ— 110Β° = r2 Γ— 110Β° Γ— πœ‹/(180Β°) = r2 Γ— 11πœ‹/18 Given that Length of I arc = length of II arc r1 Γ— 13πœ‹/36 = r2 Γ— 11πœ‹/18 π‘Ÿ1/π‘Ÿ2 = 11π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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