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 $2(x+y+z)=5+6+7=18$
$\Rightarrow x+y+z=9$.....(4)
Using (1) in (4), we have $5+z=9\Rightarrow z=4$
Now using,
(3) $\Rightarrow x=7-z=7-4=3$
And
(2.1) $\Rightarrow y=6-z=6-4=2$
Therefore, the radii of the circles are 3 cm, 2 cm and 4 cm.