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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.
Radius of one of the circles, C1 = 19 cm = r1
Radius of the other circle, C2 = 9 cm = r2
Let the other circle be C with radius ‘r’.
Circumference of C = Circumference of C1 + Circumference of C2 …………(i)
∵ Circumference of circle = 2πr
∴ Circumference of C1 = 2πr1 = 2 × × 19 =
and Circumference of C2 = 2πr2 = 2 × × 9 =
Using (i), we have
2πr = + =
2 × × r =
r = × × = 28
r = 28 cm
Hence, the radius of the circle is 28 cm.