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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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