# If the sum of the areas of two circles with radii

Question:

If the sum of the areas of two circles with radii $r_{1}$ and $r_{2}$ is equal to the area of a circle of radius $r$, then $r_{1}^{2}+r_{2}^{2}$

(a) $>r^{2}$

(b) $=r^{2}$

(c) $<\mathrm{r}^{2}$

(d) None of these

Solution:

We have given area of the circle of radius r1 plus area of the circle of radius r2 is equal to the area of the circle of radius r.

Therefore, we have,

$\pi r_{1}^{2}+\pi r_{2}^{2}=\pi r^{2}$

Cancelling, we get

$r_{1}^{2}+r_{2}^{2}=r^{2}$

Therefore, $r_{1}^{2}+r_{2}^{2}=r^{2}$.

Hence, the correct answer is option (b).