Question

Abc is a right angled triangle with bc = 6 cm and ab = 8 cm. ac is hypotenuse. a circle with centre o and radius x has been inscribed. what is the value of x.

Answer 1

In Given Triangle ABC 
AC2+ AB2 = BC2
(6*6)+(8*8)= BC2
BC2=64+36
BC2=100
BC=10

Area of Triangle ABC= 8*6/2
                               =24 Cm2
Semiperemetre of ABC= (8+6+10)/2
                                  =12 cm 
Radius of circle=  Area Of Triangle /Semiperimeter of triangle
                       =  24/12
                        = 2 cm 
Hence Radius of circle is 2 cm 

hope it became easy to understand by the diagram...

Answer 2

Hypotenuse is 6 root 2 cm.

The sides for this will be 6 cm because it is an isosceles triangle.

2/3 rd of the length of sides that is 2 / 3 * 6 = 4cm

Now if the radius of the triangle will be dropped or reduced it will be become the perpendicular on sides.

Now it will form a square: with a side of 2 cm each ((6-4)=2)

So the radius of the circle is 2 cm.