5. If a, b and c are the sides of a right angled triangle 'c' is hypot

1.	5. If a, b and c are the sides of a right angled triangle 'c' is hypotenuse, thenprove that the radius r' of the circle which touches the sides of the triangleisa t b-c
Answer» Let the circle touches the sidesAB,BC andCA oftriangle ABCat 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

5. If a, b and c are the sides of a right angled triangle 'c' is hypotenuse, thenprove that the radius r' of the circle which touches the sides of the triangleisa t b-c

Answer»

Let the circle touches the sidesAB,BC andCA oftriangle ABCat 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