Question

A, B and C are the sides of a right triangle, where C is the hypotenuse .A circle of radius R ,touches the sides of the triangle. Provethat R is equal to (A + B - C) / 2 ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

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