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.

π - 2

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π + 2

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\frac{π}{3}

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\frac{2 π}{3}

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Solution

The correct option is A $π - 2$
Perimeter of sector with angle $θ$ is $2 r + r θ$
Length of arc of semicircle $= π r$
$⟹ 2 r + r θ = π r$ .... [Given]
$⟹ θ = π - 2$
Hence, option A is correct.

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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.

The correct option is A π−2Perimeter of sector with angle θ is 2r+rθLength of arc of semicircle=πr⟹2r+rθ=πr .... [Given] ⟹θ=π−2 Hence, option A is correct.

The correct option is A $π - 2$
Perimeter of sector with angle $θ$ is $2 r + r θ$
Length of arc of semicircle $= π r$
$⟹ 2 r + r θ = π r$ .... [Given]
$⟹ θ = π - 2$
Hence, option A is correct.