In the figure (ii) given below, ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with vertices A, B and C as their centres. Find the radii of the three circles.

In the figure (ii) given below, two concentric circles with centre O are of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find BP.

In the figure (i) given below, AB = 8 cm and M is mid-point of AB. Semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all three semicircles as shown, find its radius.

In the figure (i) given below, the sides of the quadrilateral touch the circle. Prove that AB + CD = BC + DA.