RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 11 of Exercise 18A

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11

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, 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.


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