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Central angle subtended by a chord in radians and the area of the major sector of a circle

Central angle subtended by a chord in radians and the area of the major sector of a circle

6 marks

The points \(A\) and \(B\) lie on a circle with centre \(O\) and radius \(6\text{ cm}\). The chord \(\mathrm{AB}\) is \(7\text{ cm}\) long and \(\mathrm{A\hat{O}B}=\theta\), where \(0<\theta<\pi\). The major sector \(OAB\) is shaded in the diagram.

  1. Find \(\theta\) in radians.[3]
  2. Calculate the area of the shaded major sector.[3]

Solution:

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Answer:(a) \(\theta=1.25\) (b) \(90.7\text{ cm}^2\)

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