MCQ

If the sum of the areas of two circles with radii \[r_1\]and \[r_2\] is equal to the area of circle of radius \[r\] then

#### Options

\[r = r_1 + r_2\]

\[{r_1}^2 + {r_2}^2 = r^2\]

\[r_1 + r_2 < r\]

\[{r_1}^2 + {r_2}^2 < r^2\]

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#### Solution

The radius of the two circles are \[r_1 \text{ and } r_2\] Now, according to the given condition

Area of circle with radius r = Area of circle with radius \[r_1\]+ Area of circle with radius \[r_2\]

\[\pi r^2 = \pi r_1^2 + \pi r_2^2 \]

\[ \Rightarrow r^2 = r_1^2 + r_2^2\]

Concept: Area of Circle

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