two circles touch internally and the sum of their areas is 116*22/7cm2 and the distance betttween their centres is 6cm. find the radii of the circles?

Let the centre of the two circles be O1 and O2 and radii be r 1 = (O1A) and r 2 = (O2A).

Both touch each other of A such that O1 O2 = 6 cm

Now

O1A – O2A = O1 O2 = 6 cm

 r 1  r 2 = 6 cm ... (1)

 

also sum of area of two circles = 116 π cm2 ... (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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