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If two arcs of the same length in two circles subtend angles 65° and 110° at the centre. Find the ratio of their radii.

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Let r1 and r2 be the radii of the two circles and let their arcs of same length S subtend angles of 65° and 110° at their centres. Angle subtended at the centre of the first circle,

   θ1 = 65°= (65x π/180)° = (13π/36)°

∴ S=r1θ1= r1 (13π/36)           ...(i)

Angle subtended at the centre of the second circle,

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