If the sum of the areas of two circles with radii R_1and R_2 is equal to

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Solution

Q.
If the sum of the areas of two circles with radii $R_{1} a n d R_{2}$ is equal to the area of a circle of radius R , then:

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

2 $R_{1}^{2} + R_{2}^{2} = R^{2}$

3 $R_{1} + R_{2} < R$

4 $R_{1}^{2} + R_{2}^{2} < R^{2}$

Ans.
(2)

According to the question,

$π R_{1}^{2} + π R_{2}^{2} = π R^{2} \Rightarrow π (R_{1}^{2} + R_{2}^{2}) = π R^{2} \Rightarrow R_{1}^{2} + R_{2}^{2} = R^{2}$

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