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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) \[R_{1}^{2}+R_{2}^{2}<{{R}^{2}}\]
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) \[R_{1}^{2}+R_{2}^{2}<{{R}^{2}}\]
Areas Related to Circles | Exercise 11.1 | Maths | NCERT Exemplar
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) \[R_{1}^{2}+R_{2}^{2}<{{R}^{2}}\]

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.

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