two circles touch internally. the sum of their areas is 116pi cm.sq and the distance between their centers is 6cm . find the radii of the circles

Asked by vishnu PRIYAN | 20th Feb, 2012, 11:28: AM

Expert Answer:

Since the two circles touch each other internally, so the distance between their centers = difference of their radii

Let the radius of the larger circles be x cm

Then, radius of the smaller circle = (x - 6) cm

Therefore, Sum of their areas = ? r2 + ? (x - 6)2 = 116 ? (given)

=> x2 + x2 - 12x + 36 = 116

=> x2 - 6x - 40 = 0

=> (x - 10) (x + 4) = 0

=> x = - 4, 10.

Rejecting negative value, we have, x = 10

Therefore, the radii of the two circles are 10 cm and 4 cm.

Answered by  | 20th Feb, 2012, 11:38: AM

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