If the sum of the circumferences of two circles with radii R1and R2 is equal to the circumference of a circle of radius R, then

Given that sum of the circumferences of two circles with radii

R_{1}

and

R_{2}

is equal to the circumference of a circle of radius

R

.
Then,
Circumference of circle with radius

R_{1} = 2 π R_{1}

.
Circumference of circle with radius

R_{2} = 2 π R_{2} .

∴

The sum of circumferences,

Sum = 2 π (R_{1} + R_{2})

.
Again the circumference of circle with radius

R = 2 πR .

∴

By given condition,

2 π (R_{1} + R_{2}) = 2 πR

⟹ R_{1} + R_{2} = R

.
Hence, if the sum of the circumferences of two circles with radii

R_{1}

and

R_{2}

is equal to the circumference of a circle of radius

R

, then

R_{1} + R_{2} = R

.
Therefore, option 1 is correct.

If the sum of the circumferences of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle of radius $R$ , then