Question

If a b, and c are the sides of a right angled triangle where c is the hypotenuse, then prove that
the radius r of the circle which touches the sides of the triangle is given by r = a+b-c÷2

Answer 1

bg=be, cg=cf, af=ae (tangents from same point)
ed=dg=r
bgde is an square.

cg=cf=a-r
ae=af=c-r
b=a-r + c-r
b+2r=a+c
2r=a+c-b
r=a+c-b/2