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Last updated at Feb. 17, 2020 by Teachoo
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 π = r ΞΈ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle π = r1 ΞΈ = r1 Γ 65Β° = r1 Γ 65Β° Γ π/(180Β°) = r1 Γ 13π/36 Length of arc of 2nd circle π = r2 ΞΈ = r2 Γ 110Β° = r2 Γ 110Β° Γ π/(180Β°) = r2 Γ 11π/18 Given that Length of I arc = length of II arc r1 Γ 13π/36 = r2 Γ 11π/18 π1/π2 = 11π/18 Γ 36/13π π1/π2 = 22π/13π π1/π2 = 22/13 Hence r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13