Book: NCERT - Mathematics
Chapter: 12. Areas Related to Circles
Subject: Maths - Class 10th
Q. No. 1 of Exercise 12.1
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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.
Radius (r1) of 1st circle = 19 cm
Radius (r2) or 2nd circle = 9 cm
Now,
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:
Circumference of 3rd circle = Circumference of 1st circle + Circumference of 2nd circle
2πr = 38π + 18π = 56π
r = 
= 28
Therefore, the radius of the circle which has circumference equal to the sum of the circumference of the given two circles is 28 cm
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