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# The radii of two circles are(19;cm) and (9;cm)respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles(.)

## QuestionMathClass 10

The radii of two circles are$$19\;cm$$ and $$9\;cm$$respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles$$.$$

28 cm
4.6     4.6     ## Solution

Let $$r_{1}=19\;cm$$ and $$r_{2}=9\;cm$$and r be the radius of new circle$$.$$
$$\therefore$$Circumference of $$1^{st}$$ circle$$,$$
$$C_{1}=2\pi r_{1}=2\pi \times 19=38\pi\; cm$$
and circumference of $$2^{nd}$$ circle$$,$$
$$C_{2}=2\pi r_{2}=2\times \pi \times 9=18\pi\; cm$$
According to the given condition$$,$$
Circumference of new circle $$=$$ Circumference of $$1^{st}$$ circle$$+$$ Circumference of $$2^{nd}$$ circle
$$\therefore$$   $$2\pi r=38\pi +18\pi$$
$$\Rightarrow 2\pi r=56\pi$$
$$\Rightarrow$$$$r=\frac {56\pi }{2\pi }=28\;cm$$
Hence$$,$$ radius of new circle is$$28cm.$$          