Question

If the sum of the circumferences of two circles with radii ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ is equal to the circumference of a circle of radius $R$, then

• A. $R_1+R_2=R$
• B. $R_1+R_2>R$
• C. $R_1+R_2<R$
• D. Nothing definite can be said about the relation among $R_1,R_{2}andR.$

Answer 1

The correct option is A

$R_1+R_2=R$

Explanation for correct option:

We know that for a circle of radius $R$circumference of the circle is $2\mathrm{\pi R}$

Circumference of the circle with radius ${\mathrm{R}}_1$ = $2{\mathrm{\pi R}}_1$

Circumference of the circle with radius ${\mathrm{R}}_2$ = $2{\mathrm{\pi R}}_2$

Given that the sum of the circumferences of two circles with radii ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ is equal to the circumference of a circle of radius $R$

Let $C_1$ is the circumference of the circle with radius ${\mathrm{R}}_1$, $C_2$is the circumference of the circle with radius ${\mathrm{R}}_2$ and $C$is he circumference of a circle of radius $R$.

$\therefore C_1+C_2=C$

$$\begin{gathered} \Rightarrow 2{\mathrm{\pi R}}_1+2{\mathrm{\pi R}}_2=2\mathrm{\pi R} \\ \Rightarrow R_1+R_2=R \end{gathered}$$

Hence, option A is correct.