# 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 ______. - Mathematics

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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 ______.

#### Options

• R1 + R2 = R

• "R"_1^2 + "R"_2^2 < "R"^2

• R1 + R2 < R

• "R"_1^2 + "R"_2^2 < "R"^2

#### Solution

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 "R"_1^2 + "R"_2^2 < "R"^2.

Explanation:

Area of circle = Area of first circle + Area of second circle

∴ πR2 = πR12 + πR22

⇒ R2 = R12 + R22

Concept: Circumference of a Circle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Multiple Choice Questions | Q 11 | Page 847
NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 1 | Page 120

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