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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 find the relationship between $R_1,\ R_2$ and $R$.
Given: Sum of the circumferences of two circles with radii $R_1$ and $R_2$ is equal to the circumference of a circle of radius $R$.
To do: To find the relationship between $R_1,\ R_2$ and $R$.
Solution:
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 $=2\pi (R_1+R_2)$
Again the circumference of circle with radius $R=2\pi R$
$\therefore$ By given condition,
$2\pi (R_1+R_2)=2\pi R$
$\Rightarrow R_1+R_2=R$.
Updated on: 10-Oct-2022
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