Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If a region bounded by a circle $C$ is to be divided into three regions of equal areas by drawing two circles concentric with $C$, then the ratio of the radii of the two circles must be
(a)1 : 3
(b)$1: \sqrt{3}$
(c)1 : 2
(d)$1: \sqrt{2}$
Answer
Answer (as printed): D
Explanation
Let the radius of the given circle be $R$. Let the radii of the two inner circles be $R_{1}$ and $R_{2}$. $$\begin{aligned} & \text { Then, } \pi\left(R_{1}^{2}-R_{2}^{2}\right)=\pi R_{2}^{2} \\ & \Rightarrow R_{1}^{2}-R_{2}^{2}=R_{2}^{2} \\ & \Rightarrow R_{1}^{2}=2 R_{1}^{2} \Rightarrow \frac{R_{2}^{2}}{R_{1}^{2}}=\frac{1}{2} \Rightarrow \frac{R_{2}}{R_{1}}=\frac{1}{\sqrt{2}} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.