# If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then

**Question:**

If the sum of the circumferences of two circles with radii R1 and R2 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}

(d) none of these

**Solution:**

(a) $R_{1}+R_{2}=R$

Because the sum of the circumferences of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle with radius $R$, we have:

$2 \pi R_{1}+2 \pi R_{2}=2 \pi R$

$\Rightarrow 2 \pi\left(R_{1}+R_{2}\right)=2 \pi R$

$\Rightarrow R_{1}+R_{2}=R$