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Circumference of a Circle

If the sum of...

Question

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

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R_{1} + R_{2} > R

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R_{1} + R_{2} < R

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Nothing definite can be said about the relation among

R_{1}

R_{2}

and

R

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Solution

The correct option is A $R_{1} + R_{2} = R$
Circumference of the circle with radius $R_{1}$ = $2 π R_{1}$
Circumference of the circle with radius $R_{2}$ = $2 π R_{2}$
Circumference of the circle with radius $R$ = $2 π R$
Given,
$2 π R_{1} + 2 π R_{2} = 2 π R$
$=> 2 π (R_{1} + R_{2}) = 2 π R$
$=> R_{1} + R_{2} = R$

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