Assertion (A) : If the radius of sector of a circle is reduced to its half and angle is doubled then

Question

Assertion (A) : If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same.\ Reason (R) : The length of the arc subtending angle $	heta$ at the centre of a circle of radius $r=\frac{\pi r 	heta}{180}$.\

Professor PC Thomas Classes · Answer

(d): Let angle $=	heta$ and radius $=r$ Perimeter of sector of a circle $=2 r+	heta r$\ Now, angle $=2 	heta$ and radius $=\frac{r}{2}$\ Perimeter of sector of a circle $=\frac{2 	imes r}{2}+2 	heta r=r+2 	heta r$\ Hence, Assertion (A) is false but reason (R) is true.\