Question

In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is ______.

Options

• 1.5 cm

• 2 cm

• 2.5 cm

• 3 cm

Answer 1

In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is 2 cm.

Explanation:

Let the radii of the three circles be x, y, z respectively. Then,

x + y = 5, y + z = 7 and z + x = 6

⇒ 2(x + y + z) = 18

⇒ x + y + z = 9

∴ x = (x + y + z) – (y + z)

= (9 – 7)

= 2 cm