Question:
If the sum of the areas of two circles with radii R1 and R2 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}
(d) $R_{1}^{2}+R_{2}^{2}
Solution:
(b) According to the given condition,
Area of circle =Area of first circle + Area of second circle
$\therefore \quad \pi R^{2}=\pi R_{1}^{2}+\pi R_{2}^{2}$
$\Rightarrow \quad R^{2}=R_{1}^{2}+R_{2}^{2}$
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