A) \[\pi -2\]
B) \[\pi +2\]
C) \[\frac{\pi }{3}\]
D) \[\frac{2\pi }{3}\]
Correct Answer: A
Solution :
Let the radius of circle be r. \[\therefore \] Length of an arc \[=\frac{\theta }{{{360}^{o}}}\times 2\pi r\] Since, perimeter of a sector of a circle = length of the arc of the semicircle \[\therefore \] \[\frac{\theta }{{{360}^{o}}}\times 2\pi r+2r=\pi r\] \[\Rightarrow \] \[\theta +2=\pi \] \[\Rightarrow \] \[\theta =\pi -2\]
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