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.

• A. 2 cm, 3 cm, 4 cm
• B. 3 cm, 4 cm, 1 cm
• C. 1 cm, 2.5 cm, 3.5 cm
• D. 1 cm, 2 cm, 4 cm

Answer 1

The correct option is A

2 cm, 3 cm, 4 cm

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) ($\Rightarrow$ y=6-z)... (2.1)

x+z = 7 …..(3)

Adding (1), (2) and (3), we have $2(x+y+z)=5+6+7=18$

$⟹x+y+z=\mathrm{9....}\left(4\right)$

Using (1) in (4), we have $5+z=9⟹z=4$

Now using, $\left(3\right)⟹x=7-z=7-4=3$

And $\left(2.1\right)⟹y=6-z=6-4=2$

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