Question

Two circles touch externally. The sum of their areas is 130 π 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 [Fig.].
Let C₁ and C₂ be the centres of the given circles. Then,
C₁C₂ = r₁ + r₂
⇒ 14 = r₁ + r₂ [C₁C₂ = 14 cm given]
⇒ r₁ + r₂ = 14        …(i)
It is given that the sum of the areas of two circles is equal to 130 π cm^2.