Two concentric circles are such that the smaller divides the larger circle into two regions of equal areas. If the radius of the smaller circle is $2$ , then the length of a tangent from any point p on the larger circle to the smaller circle is

\sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

\sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2$
Two concentric circles are shown in figure.
From figure, we have $π r_{1}^{2} = \frac{1}{2} π r_{2}^{2}$
$\Rightarrow r_{2} = \sqrt{2} r_{1}$
Length of tangent is $\sqrt{r_{2}^{2} - r_{1}^{2}}$
$= \sqrt{2 r_{1}^{2} - r_{1}^{2}} = r_{1} = 2$

Suggest Corrections

Similar questions

In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then find the radius of the smaller circle.

Q. In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then Find the radius of the smaller circle. [CBSE 2013C]

Q. In two concentric circles, a chord length 80 cm of larger circle becomes a tangent to the smaller circle whose radius is 9 cm. The radius of the larger circle will be

Q. Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

Q. There are two circles of different radii such that radius of the smaller circle is three seventh that of the larger circle. A square whose area equals 3969 square cm has its side as thrice the radius of the larger circle. What is the circumference of the smaller circle?

Join BYJU'S Learning Program

Two concentric circles are such that the smaller divides the larger circle into two regions of equal areas. If the radius of the smaller circle is 2, then the length of a tangent from any point p on the larger circle to the smaller circle is

The correct option is B 2Two concentric circles are shown in figure.From figure, we have πr21=12πr22⇒r2=√2r1Length of tangent is √r22−r21=√2r21−r21=r1=2

Two concentric circles are such that the smaller divides the larger circle into two regions of equal areas. If the radius of the smaller circle is $2$ , then the length of a tangent from any point p on the larger circle to the smaller circle is

The correct option is B $2$
Two concentric circles are shown in figure.
From figure, we have $π r_{1}^{2} = \frac{1}{2} π r_{2}^{2}$
$\Rightarrow r_{2} = \sqrt{2} r_{1}$
Length of tangent is $\sqrt{r_{2}^{2} - r_{1}^{2}}$
$= \sqrt{2 r_{1}^{2} - r_{1}^{2}} = r_{1} = 2$