Question

Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm, and 7 cm. Find the radii of the circles. 

Options

• 2 cm, 3 cm, 4 cm

• 1 cm, 2 cm, 4 cm

• 1 cm, 2.5 cm, 3.5 cm

• 3 cm, 4 cm, 1 cm

Answer 1

2 cm, 3 cm, 4 cm

Explanation:

Consider the below figure wherein three circles touch each other externally.

Since the distances between the centres of these circles are 5 cm, 6 cm, and 7 cm respectively, we have the following set of equations with respect to the above diagram:

x + y = 5 …..(1)

y + z = 6 …… (2) (⇒ y = 6 - z)… (2.1)

x + z = 7 …..(3)

Adding (1), (2) and (3),

we have 2(x + y + z) = 5 + 6 + 7 = 18

⇒ x + y + z = 9 …. (4)

Using (1) in (4),

we have 5 + z = 9

⇒ z = 4

Now using, (3)

⇒ x = 7 − z = 7 − 4 = 3 And (2.1)

⇒ y = 6 − z = 6 − 4 = 2

Therefore, the radii of the circles are 3 cm, 2 cm, and 4 cm.