Question

If a,b,c are the sides of a right triangle where c is the hypo. Then the radius r of the circle which touches the side of the triangle is 1) r=(a+b+c)/2
2) r=(b+c-a)/2 3) r=(a+b-c)/2
4) r=a+b-(c/2)

Answer 1

Hey mate,

Let the circle touches the sides  AB,BC and CA of triangle ABC at D, E and F 

Since lengths of tangents drawn from an external point are equal  We have

 AD=AF,  BD=BE  and CE=CF

Similarly EB=BD=r

Then we have  c = AF+FC

                   ⇒ c = AD+CE

                   ⇒ c = (AB-DB)(CB-EB)

                   ⇒ c = a-r +b-r

                   ⇒ 2r =a+b-c

                        r =( a+b-c)/2

Hope it will help you.

✨It's M.S.V.

Answer 2

Answer:

Step-by-step explanation:

Since lengths of tangents drawn from an external point are equal  We have

 AD=AF,  BD=BE  and CE=CF

Similarly EB=BD=r

Then we have  c = AF+FC

                   ⇒ c = AD+CE

                   ⇒ c = (AB-DB)(CB-EB)

                   ⇒ c = a-r +b-r

                   ⇒ 2r =a+b-c

                        r =( a+b-c)/2