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COMEDK · Maths · 8. Trigonometric Ratios & Identities

-The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sector in radians is

  1. A \(\pi-2\)
  2. B \(\pi+2\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\frac{2 \pi}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\pi-2\)

Step-by-step Solution

Detailed explanation

It is given that, Perimeter of sector \(=\) Length of arc of the semi-circles \(\begin{array}{ll}\Rightarrow & 2 r+l=\pi r \\ \Rightarrow & 2 r+r \theta=\pi r \quad[l l=r \theta] \\ \Rightarrow & r(2+\theta)=\pi r \\ \Rightarrow & \theta=\pi-2\end{array}\)