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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.

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Radius = 33 cm


\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.

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