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.

 

plzzzzz ans!!!! its urgent!!!

 

Let the centre of the two circles be O1 and O2 and radii be r1 = (O1A) and  r2 = (O2A).

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

Now

O1A – O2A = O1 O2 = 6 cm

r1r2 = 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 r1 = 10

 

putting the value of r1 in (4) we get

 

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

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