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Question:

If the length of a minor arc AB of a circle is 1/4 of its circumference, then the angle subtended by the minor arc AB at the center will be?

30

45

60

90

Solution:

Length of the minor arc AB = πrθ/180, where θ is the angle subtended by AB at the centre
∴ 1/4 × circumference = πrθ/180
∴ 1/4 × 2πr = πrθ/180
∴ 1/4 × 2πr × 180/πr = θ
∴ θ = 90o