# If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then ______. - Mathematics

MCQ
Sum

If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then ______.

#### Options

• R1 + R2 = R

• R1 + R2 > R

• R1 + R2 < R

• Nothing definite can be said about the relation among R1, R2 and R.

#### Solution 1

R+ R2 = R

Because the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle with radius R, we have:

2pi"R"_1 + 2pi"R"_2 = 2pi"R"

=> 2pi("R"_1 +"R"_2) = 2pi"R"

=> "R"_1 + "R"_2 = "R"

#### Solution 2

If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then R1 + R2 = R.

Explanation:

We are given that

Circumference of circle with radius R = Circumference of first circle with radius R1 + Circumference of second circle with radius R2

∴ 2πR = 2πR1+ 2πR2

⇒ R = R1+ R2

Concept: Circumference of a Circle
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 2 | Page 120
RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Multiple Choice Questions | Q 12 | Page 847

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