Q1. Two circles touch internally, the sum of their areas is 116 π. Distance between their center is 6 cm. Find the radii of circles.
Solution:
Let the radius of small circle = r cm.
Then the radius of Large circle R = 6 + r cm.
Sum of their areas = 116π cm
πR2 + πr2 = 116 π cm
π(R2+ r2) = 116π
R2+ r2 = 116
(6 + r)2 + r2 = 116
36 + r2 + 12r + r2 = 116
2r2 + 12r + 36 = 116