Question

. The sides a, b, c of a right triangle,where c is the hypotenuse, are circumscribe in a

circle. Prove that the radius r of the circle is given by r = a+b-c/2​

Answer 1

Let the circle touches sides AB,BC and CA at F,D and E respectively where AB=c,BS=a and AC=b

Length of the tangents drawn from an external point are equal.

AE=AF

BD=BF

CE=CD=r

b−r=AF

a−r=BF

So, AB=AF+BF

c=b−r+a−r

c=a+b−2r

2r=a+b−c

r=

2

a+b−c