ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centers. Find the radii of the three circles.

Solution:

According to the given question,

ABC is a triangle with

   

Three circles are drawn with centre

   

touch each other at

   

respectively.

So, we need to find the radii of the three circles.

Let,

   

   

   

So, we have

   

   

   

Adding all the three equations, we have

   

   

Subtracting (i), (ii) and (iii) from (iv) we get

   

   

And,

   

Thus, radii of the three circles are