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Question
Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.
Solution
Let R be the radius of the big circle.
The radii of two circles are r1 = 3cm and r2 = 4cm
Now,
Circumference of big circle
= Sum of circumference of circles of radii r1 and r2
⇒ 2πR = 2πr1 + 2πr2
⇒ R = r1 + r2
⇒ R
= 3 + 4
= 7cm
∴ Area of big circle
= πR2 = `(22)/(7) xx 7 xx 7`
= 154cm2.
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