Question

3. If a, b, c are the sides of a right triangle where c is the hypotenuse, prove that the radius of the circle which touches all the sides of the triangle is given by a + b -c/
2 .

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Answer 1

Step-by-step explanation:

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