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.