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

Given:

Radius of one of the circles, C_{1} = 19 cm = r_{1}

Radius of the other circle, C_{2} = 9 cm = r_{2}

Let the other circle be C with radius ‘r’.

Circumference of C = Circumference of C_{1} + Circumference of C_{2} …………(i)

∵ Circumference of circle = 2πr

∴ Circumference of C_{1} = 2πr_{1} = 2 × × 19 =

and Circumference of C_{2} = 2πr_{2} = 2 × × 9 =

Using (i), we have

2πr = + =

2 × × r =

r = × × = 28

r = 28 cm

__Hence, the radius of the circle is 28 cm.__

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