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

A
R1+R2=R
B
R1+R2>R
C
R1+R2<R
D
Nothing definite can be said about the relation among R1,R2 and R.

Solution

## The correct option is A $$R_{1}+R_{2}=R$$The  circumference of circle with radius $${ R }_{ 1 }=2\pi { R }_{ 1 }$$.and the circumference of circle with radius$${ R }_{ 2 }=2\pi { R }_{ 2 }.$$ $$\therefore$$ The Sum of Circumferences, $$Sum=2\pi \left( { R }_{ 1 }+{ R }_{ 2 } \right)$$ .Again the circumference of circle with radius $${ R }=2\pi { R }.$$$$\therefore$$ By given condition,$$2\pi \left( { R }_{ 1 }+{ R }_{ 2 } \right) =2\pi { R }\Longrightarrow { R }_{ 1 }+{ R }_{ 2 }=R$$.Mathematics

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