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Question
Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.
Solution
Radius of first circle = r1 = 15 cm
Radius of second circle = r2 = 18 cm
∴ Circumference of first circle = 2πr1 = 30π cm
Circumference of second circle = 2πr2 = 36π cm
Let the radius of the circle = R
According to the question,
Circumference of circle = Circumference of first circle + Circumference of second circle
2πR = 2πr1 + 2πr2
⇒ 2πR = 30π + 36π
⇒ 66π
⇒ R = 33
⇒ Radius = 33 cm
Hence, required radius of a circle is 33 cm.
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