Question

IF a,b,c are the sides of a right triangle where c is the hypotenuse, 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

Answer:

Let the circle touches the sides BC,CA,AB of the right triangle ABC at

D,E and F respectively, where BC=a, CA=b and AB=c.

Then, AE=AF and BD=BF. Also CE=CD=r.

b-r =AF, a-r=BF

or AB =c=AF+BF = b-r+a-r

r =