Solve fast:
21. Two circles touch internally. The sum of their areas is 116 cm2 and the distance between their centres is 6 cm. Find the radis of the circlm.
22. If 1+4+7+10+.....+x=287, find the value of x.
Hi,
22:
21;-
22:
1 + 4 + 7 + 10 +.... + x = 287
Let there be n terms in the A.P.
Let there be n terms in the A.P.
21;-
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.