1.r= 1/2(AB+AC-BC) (formula 1)

Using the properties of tangents.

a=BD+CD=BF+CE=c-r+b-r

So r=(c+b-a)/2.

2. Find the area method

On the one hand, S=bc/2

On the other hand, triangle ABC can be divided into three small triangles with O as the common vertex.

So S=r(a+b+c)/2.

So BC = r (a+b+c)

r=bc/(a+b+c).