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Areas Related to Circles
NCERT Exemplar
CBSE
Grade 10

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:
(a) $R_1 + R_2 = R$
(b) $R_1^2 + R_2^2 = R^2$
(c) $R_1 + R_2 < R$
(d) $R_1^2 + R_2^2 < R^2$

Step-by-Step Solution

Key Concept: $\\pi R_1^2 + \\pi R_2^2 = \\pi R^2 \\Rightarrow R_1^2 + R_2^2 = R^2$.
$\pi R_1^2 + \pi R_2^2 = \pi R^2 \Rightarrow R_1^2 + R_2^2 = R^2$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Cancelling $\pi$ to get $R_1^2 + R_2^2 = R^2$: 1.0 Mark

Correct Answer: $R_1^2 + R_2^2 = R^2$
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