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1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
The radius of the 1st circle = 19 cm (given) ∴ Circumference of the 1st circle = 2π×19 = 38π cm The radius of the 2nd circle = 9 cm (given) ∴ Circumference of the 2nd circle = 2π×9 = 18π cm So, The sum of the circumference of two circles = 38π+18π = 56π cm Now, let the radius of the 3rd circle = R ∴ The circumference of the 3rd circle = 2πR It is given that sum of the circumference of two circles = circumference of the 3rd circle Hence, 56π = 2πR Or, R = 28 cm.

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