circle

The sum of the areas of two circles is 116π cm2 (refer diagram below). the centre of the circles is 6 cm apart. find the radius of the circles.

Let the radius of big circle = x

So radius of small circle = x -6

Π (x² + (x – 6)²) = 116 Π

Or 2x² – 12x – 80 = 0

Or x = 10, ignoring the negative value of -4.

So, the two radii’s are 10 and 4 cm.