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-----

• A. $1.5$ cm
• B. $2$ cm
• C. $2.5$ cm
• D. $3$ cm

Answer 1

The correct option is B $2$ cm

Let the radius of the circles centred at $A$, $B$ and $C$ be $x,y,z$ respectively.

As the circles touch each other externally and as given $AB=5\Rightarrow x+y=5$......(1) and $BC=7\Rightarrow y+z=7$.......(2) and $CA=6\Rightarrow x+z=6$.......(3).

Now adding (1),(2) and (3) we get,

$2(x+y+z)=18$

or, $x+y+z=9$.......(4).

Now subtracting (2) from (4) we get,

$x=2$.

So, the radius of the circle centred at $A$ is $2$ cm.