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

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Solution

The radius of the two circles are $r_{1} and r_{2}$ .
Now, according to the given condition
Area of circle with radius r = Area of circle with radius $r_{1}$ + Area of circle with radius $r_{2}$
${πr}^{2} = {πr}_{1}^{2} + {πr}_{2}^{2} \Rightarrow r^{2} = r_{1}^{2} + r_{2}^{2}$
Hence, the correct answer is option (b).

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