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 O1 and O2 and radii be r1 = (O1A) and  r2 = (O2A).

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


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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