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in Areas Related To Circles by (56.3k points)

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

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Best answer

Given,

Radius of circle 1 = r1 = 19 cm

Radius of circle 2 = r2 = 9 cm

We know that, the circumference of a circle (C) = 2πr

So, C1 = 2πrand C2 = 2πr2

Let the radius be r of the circle which is to be found and its circumference (C)

Now, from the question

C = C1 + C2

2πr = 2πr1 + 2πr2

r = r1 + r[After dividing by 2π both sides]

r = 19 + 9

r = 28 cm

Thus, the radius of the circle = 28 cm

So, the area of required circle = πr2 = (22/7) × 28 × 28 = 2464 cm2

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