The perimeter of a certain sector of a circle is equal to half of the circle of which it is a sector. The circular measure of one angle of the sector is:

(π - 2)

radian

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(π + 2)

radian

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π

radian

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(π - 3)

radian

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Solution

The correct option is A $(π - 2)$ radian
Let length of Arc $A B = P$ .
$\Rightarrow$ $P + r + r =$ $\frac{2 π r}{2}$ (Given).
$\Rightarrow$ $P + 2 r =$ $π r$ .
$\Rightarrow$ $r O + 2 r =$ $π r$ .
$\Rightarrow$ $O =$ $π$ $- 2$ .
$∴$ A) Answer.

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The perimeter of a certain sector of a circle is equal to half of the circle of which it is a sector. The circular measure of one angle of the sector is:

The correct option is A (π−2) radianLet length of Arc AB=P.⇒ P+r+r= 2πr2 (Given).⇒ P+2r= π r. ⇒ rO+2r= π r.⇒ O= π −2.∴ A) Answer.

The correct option is A $(π - 2)$ radian
Let length of Arc $A B = P$ .
$\Rightarrow$ $P + r + r =$ $\frac{2 π r}{2}$ (Given).
$\Rightarrow$ $P + 2 r =$ $π r$ .
$\Rightarrow$ $r O + 2 r =$ $π r$ .
$\Rightarrow$ $O =$ $π$ $- 2$ .
$∴$ A) Answer.