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
⇒ r1 – r2 = 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.