Question

Two circle touches internally.the sum there are is 116cm and distance between the centre is 6 find radius

Answer 1

A/q ,
area of 1st circle + area of 2nd circle
circle = 116 cm^2
= πr^2 + πR^2 = 116π
= π( R^2 + r^2 ) = 116 π
= R^2 + r^2 = 116 ...........1)
= distance is given = 6cm
i.e... R-r =6
R= r+6 ............2)

now from eqn 1 and 2nd ,
= (r+6)^2 +r^2 = 116
= r^2 +10r - 4r - 40 =0
= r^2 + 6r - 40 = 0
= ( r+10 ) (r-4) =0
hence r = 4 cm
so its R = 4 + 6 = 10 cm