Question

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

Answer 1

In the figure, let $AB=5cm,BC=6cm$ and $AC=7cm$

$\Rightarrow x+y=5$ …..(i)

$y+z=6\Rightarrow y=6-z$

Substituting in (i), we get,

$x+6-z=5$

$\Rightarrow x-z=-1$ …..(ii)

Also, $x+z=7$ …..(iii)

Adding (ii) and (iii), we get,

$2x=6\Rightarrow x=3,y=2,z=4$

Therefore, the radii of the circle is $2,3$ and $4cm$