If a, b , c are the sides of right triangle where v is the hypotenuse then prove that the radius of circle which touches the sides of the triangle is given by a+b-c/2
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If a b c are sides of a 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
Sol:

Sol:
The circle touches the sides BC, CA, AB of the right triangle ABC at D, E and F respectively.
Assume BC = a, CA = b and AB = c
Then AE = AF and BD = BF, CE = CD .
OE = OD = OF = r.
Here OEDC is a square then CE = CD = r.
i.e., b – r = AF, a – r = BF
or AB = c = AF + BF = b – r + a – r
∴ r = (a + b - c )/2
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