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Two circles touch internally. The sum of their areas is $116 π c m 2$ and the distance between their centers is 6 cm. Find the radii of the circles.

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4 cm and 10 cm

5 cm and 10 cm

10 cm and 5 cm

10 cm and 12 cm

answer is A.

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Detailed Solution

Given:
Two circles touch internally. The sum of their areas

116 π c m 2

is and the distance between their centers is 6 cm. To find the radii of the circles.
If r is the radius of the circle, then the area of the circle is given by,

A = π r 2

Let the radius of inner circle is

r 1

and outer circle is

r 2

Given that the distance between their centers is 6 cm, i.e.,

r 2 − r 1 = 6

r 2 = 6 + r 1

.......(1) The sum of their areas

= 116 π c m 2

Length is not negative, so

r 1 = 4

cm From equation (1),

r 2 = 6 + (4) ⇒ r 2 = 10 c m

The radii of the circles are 4 cm and 10 cm.
So, the correct option is 1.

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