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

Radius = 33 cm

Solution

$\because$  Circumference of circle =$2 \pi r$

The radii of the two circles are $r_{1}=15 cm$  and $r_{2}=18 cm$

Let the circumference of these two are $C_{1}$ and $C_{2}$  respectively.

Let the circumference of required circle is C with radius R.

So according to question $C=C_{1}+C_{2}$
$2 \pi R=2 \pi r_{1}+2 \pi r_{2}\; \; \; \; \; \; \; \; (\because C=2 \pi r)\\ 2 \pi R=2 \pi(15+18)\\ R=33 cm$

Hence the radius of the required circle is 33cm.