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.

Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centres is 12 cm. Find the diameters of the circle.

Sakshi drew a rangoli design for a competition as shown below:

Circles C₁, C₂, C₃ and C₄ have a common centre P.

The radius of circle C₁ = 6 cm.

The table given below shows the radii of the circles in terms of the radius of circle C₁.

(i) The circumference of circle C₂ is :

(a) 12π cm
(b) 24π cm
(c) 15π cm
(d) 20π cm

(ii) The area enclosed between C₁ and C₂ and also between C₃ and C₄ has been painted.

What area of the rangoli has been painted ?

(a) 85π cm²
(b) 108π cm²
(c) 324π cm²
(d) 846π cm²