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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 - Mathematics

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 \[r_2\]

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

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Q 50 | Page 74
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