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).