Question

Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

Answer 1

If two circles touch externally, then the distance between their centres is equal to the sum of their radii.

Let the radii of the two circles be r₁ cm and r₂ cm
respectively. (see fig.)
Let C₁ and C₂ be the centres of the given circles. Then,

It is given that the sum of the areas of two circles is equal to 130 π cm².

Solving (i) and (iv), we get r₁ = 11 cm and r₂ = 3 cm.

Hence, the radii of the two circles are 11 cm and 3 cm.