If the sum of the areas of two circles
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) $R_{1}+R_{2}<R$

(d) $R_{1}^{2}+R_{2}^{2}<R^{2}$

Solution:

(b) According to the given condition,
Area of circle =Area of first circle + Area of second circle

$\therefore \quad \pi R^{2}=\pi R_{1}^{2}+\pi R_{2}^{2}$

$\Rightarrow \quad R^{2}=R_{1}^{2}+R_{2}^{2}$