Question

In the adjoining figure,three circles with centre A,B and C respectively touch each other externally.if, AB=5cm,BC=7cm and CA=6cm,then find the radius of the circle with centre A.​

Answer 1

Answer:

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⇒x+y=5......(1) and BC=7⇒y+z=7.......(2) and CA=6⇒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.