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Circumference of the 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 $R_{1} + R_{2} = R$
The circumference of circle with radius $R_{1} = 2 π R_{1}$ .
and the circumference of circle with radius $R_{2} = 2 π R_{2} .$
$∴$ The Sum of Circumferences, $S u m = 2 π (R_{1} + R_{2})$ .
Again the circumference of circle with radius $R = 2 π R .$
$∴$ By given condition,
$2 π (R_{1} + R_{2}) = 2 π R ⟹ R_{1} + R_{2} = R$ .

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