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# Find the radius of a circle whose circumference is equal to the sum of the circumferences of two radii $15\ cm$ and $18\ cm$.

**Given:**A circle whose circumference is equal to the sum of the circumferences of two radii $15\ cm$ and $18\ cm$.

**To do:**To find the radius of the circle.

**Solution:**

The radii of two circles are $r_1=15\ cm$ & $r_2=18\ cm$.

The radius $r$ of the circle whose circumference $C=C_1+C_2$.

We have $C_1=2\pi r_1$ & $C_2=2\pi r_2$.

$\therefore$ The resulting circumference $C=2\pi r=C_1+C_2=2\pi (r_1+r_2)$

$=2\pi ( 15+18)\ cm=66\pi \ cm$.

$\therefore$ We have, $2\pi r=66\pi$

$\Rightarrow r=\frac{66}{2}\ cm=33\ cm$.

Thus, the radius of the circle is $33\ cm$.

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