Question

Two circles touch internally. The sum of thier area is 116π cm. Distance between thier center is 6 cm. Find the radii.

Answer 1

Answer: 10 cm

Step-by-step explanation:

R-r=6cm.

R=r+6

πR^2+πr^2=116π.

π(R^2+r^2) =116π.

(R^2+r^2) =116.

{(r+6)^2+r^2}=116.

r^2+36+12r+r^2=116.

2r^2+12r+36–116=0.

2r^2+12r-80=0.

r^2+6–40=0.

(r+10) (r-4) =0.

r=4(Neglecting r=-10.)

R=4+6=10 cm.