Q. 14.4( 19 Votes )

If a, b and c are

Answer :

The figure is given below:



Let the circle touches the sides BC, CA, AB of the right triangle ABC (right angled at C) at D, E and F respectively,


where BC = a, CA = b , AB = c respectively


Since lengths of tangents drawn from an external point are equal


Therefore, AE = AF,


and BD = BF


Also CE = CD = r and b - r = AF,


a - r = BF


Therefore AB = AF + BF


c = b - r + a - r


AB = c = AF + BF


= b - r + a - r


hence, r =


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