# The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle

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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.

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Radius (r1) of 1st circle = 19 cm

Radius (r2) or 2nd circle = 9 cm

Let the radius of 3rd circle be r.

Circumference of 1st circle = 2πr1 = 2π (19) = 38π

Circumference of 2nd circle = 2πr2 = 2π (9) = 18π

Circumference of 3rd circle = 2πr

Given that,

Circumference of 3rd circle = Circumference of 1st circle + Circumference of 2nd circle

2πr = 38π + 18π = 56π

Therefore, the radius of the circle which has circumference equal to the sum of the circumference of the given two circles is 28 cm.