An arc AB of a circle subtends an angle x radians at the

Home » Aptitude » Mensuration » Question

An arc AB of a circle subtends an angle x radians at the centre of the circle. Given that the area of the secctor AOB is equal to the square of the length of the arc AB, then the value of x is :

Let the length of arc AB be y units and radius of circle be r units.
∠AOB = x radians

∴ θ =	l
	r

⇒ x =	y	......(i)
	r

Again area of sector AOB

=	θ	× πr² =	x	r² sq units
	2π		2

According to the question,

xr²	= y² = (xr)² [From equation(i)]
2

⇒	xr²	= x²r²
	2

⇒ x =	1
	2