Question

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.

Answer 1

explaination of the answer is given

Answer 2

Given :

$r_1 = 9cm \\\\r_2 = 19cm$

To find :

Let the radius of new circle = r

According to the Question :

Circumference of required Circle = Sum of the Circumference of the two Circles

Circumference of Smaller Circle :

$2\pi r_1$

$2\pi * 9$

= $18\pi$

Circumference of Larger Circle :

$2\pi r_2$

$2\pi*19$

= $38\pi$

Now ,

Circumference of required Circle = Sum of the Circumference of the two Circles

$2\pi r = 18\pi + 38\pi$

$2\pi r = 56\pi$

$r = \frac{56\pi }{2\pi }$

$r = 28$