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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,

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R 1 + R 2 = R

R 1 + R 2 > R

R 1 + R 2 < R

Not definite can be said about the relation among

R 1, R 2

and

R

answer is A.

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Detailed Solution

Given that, the sum of the circumference of 2 circles is equal to the circumference of another circle.
The general equation of the circle is,

x − h 2 + y − k 2 = r 2

, where

h, k

are coordinates of the center and

r

is the radius of the circle.
The circle with radius

R 1

C 1 = 2 π R 1

, the circumference of the circle with radius

R 2

C 2 = 2 π R 2

and circumference of the circle with radius

R

C = 2 π R

.
Equate the sum of the circumference C

1 .

and C

2

with

C

to obtain the relation between the radius of the circles.

C 1 + C 2 = C

\Rightarrow 2 πR_{1} + 2 πR_{2} = 2 πR

\Rightarrow 2 π (R_{1} + R_{2}) = 2 πR

\Rightarrow R_{1} + R_{2} = R

Hence, option 1) is correct.

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