Total length of arc AB and arc CD is (5πr)/6
How to find length of arc of circle
Given
θ = 60⁰
OA = r cm
OA : OC = 2:3
OA/OC = 2/3
r/OC = 2/3
OC = 3r/2
Length of arc = θ/360*2πr
where
θ is angle subtended at the center by the arc
r is the radius of the circle
π is a constant
Length of arc AB = 60/360 x 2πr
AB = πr/3
Length of arc CD = 60/360 * 2π(3r/2)
= 1/6 * 3πr
= πr/2
Total length of arc AB and arc CD
= πr/3 + πr/2
= (2πr + 3πr)/6
= (5πr)/6
Total length of arc AB and arc CD is (5πr)/6