a, b and C are the sides of a right triangle, where c is the hypotenuse. A circle of radius r is, touches the side of triangle.
Prove that
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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
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