The Correct option is (B) \[R_{1}^{2}+R_{2}^{2}={{R}^{2}}\]
Explanation:
From the given question,
We got sum of the areas of two circles with radii \[R1\] and \[R2\] is equal to the area of a circle of radius \[R\]
That is Area of circle of radius \[R\]= Area of first circle of radius \[{{R}_{1}}\] + Area of second circle of radius \[{{R}_{2}}\]
Therefore, \[\pi {{R}^{2}}=\pi R_{1}^{2}+\pi R_{2}^{2}\]
We get \[{{R}^{2}}=R_{1}^{2}+R_{2}^{2}\]
Therefore, Option B is correct.