two circles touch internally, the sum of their areas is 116 pie sq cm and distances between their centres is 6cm. find the radii of the circles.

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Let the centre of the two circles be O_{1} and O_{2} and radii be *r*_{1} = (O_{1}A) and *r*_{2} = (O_{2}A).

Both touch each other of A such that O_{1} O_{2 }= 6 cm

Now

O_{1}A – O_{2}A = O_{1} O_{2 }= 6 cm

⇒ *r*_{1} – *r*_{2} = 6 cm ... (1)

also sum of area of two circles = 116 π cm^{2} ... (2)

Equating (2) and (3) we get

from (1) and (4) we get

Since radius cannot be negative

Hence *r*_{1} = 10

putting the value of *r*_{1 }in (4) we get

Hence the radii of the circles are 4 cm and 10 cm.

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