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Home » The radii of two circles are and respectively. Find the radius and area of the circle which has circumferences is equal to sum of the circumference of two circles.
The radii of two circles are 19cm and 9cm respectively. Find the radius and area of the circle which has circumferences is equal to sum of the circumference of two circles.
Areas Related To Circles | CBSE | Class 10 | Exercise 15.1 | Maths | RD Sharma
The radii of two circles are 19cm and 9cm respectively. Find the radius and area of the circle which has circumferences is equal to sum of the circumference of two circles.

As, per the question it is given that

Radius of circle 1={{r}_{1}}=19cm

Radius of circle 2={{r}_{2}}=9cm

We all know that formula for finding, the circumference of a circle (C) =2\pi r

Thus, {{C}_{1}}=2\pi {{r}_{1}} C1 = 2πr1 and {{C}_{2}}=2\pi {{r}_{2}}

Assume the radius be r of the circle which is to be found and its circumference (C)

Then, from the question it is given

C={{C}_{1}}+{{C}_{2}}

2\pi r=2\pi {{r}_{1}}+2\pi {{r}_{2}}

r={{r}_{1}}+{{r}_{2}} [After dividing by 2\pi both sides]

r=19+9

r=28cm

Therefore, the radius of the circle =28cm

Thus, the area of required circle =\pi {{r}^{2}}=\left( 22/7 \right)\times 28\times 28=2464c{{m}^{2}}

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