Question

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.

Answer 1

R₁ + 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"`

Answer 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