# Ex.12.1 Q1 Areas Related to Circles Solution - NCERT Maths Class 10

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## Question

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

## Text Solution

What is known?

What is unknown?

Radius of $$3^\rm{rd}$$ circle.

Reasoning:

Using the formula of circumference of circle $${C = 2}\pi r$$ we find the radius of the circle.

Steps:

Radius $$({r_1})$$of $$1^ \rm{st}$$ circle $$= 19 \,\rm{cm}$$

Radius $$({r_2})$$ or $$2^\rm{nd}$$ circle $$=9\,\rm{cm}$$

Let the radius of $$3^ \rm{rd}$$ circle be $$r.$$

Circumference of $$1^\rm{st}$$circle $$= 2 \pi{{\text{r}}_{\text{1}}}{\text{ = 2 }}\pi (19) = 38 \pi$$

Circumference of$$2^\rm{ nd }$$ circle $$= 2 \pi{{\text{r}}_{\text{2}}}{\text{ = 2 }}\pi (9) = 18 \pi$$

Circumference of $$3^\rm{rd}$$circle $$=2\pi r$$

Given that,

Circumference of $$3^\rm{rd}$$ $$\rm{}circle$$ $$=$$ Circumference of $$1^\rm{st }$$ $$\rm{}circle$$ $$+$$Circumference of $$2^\text{nd}$$$$\rm{}circle.$$

\begin{align} 2 \pi r &=38 \pi+18 \pi \\ &=56 \pi \\ r &=\frac{56 \pi}{2 \pi} \\ &=28 \end{align}

Therefore, the radius of the circle which has circumference equal to the sum of the circumference of the given two circles is $$28\, \rm{cm.}$$

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