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Answer»

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

So, AE = AF and BD = BFAlso CE = CD = rand b-r = AF, a- r = BF

Therefore, AB = AF + BFc = b-r + a-r

Hence, r = a+b-c/2



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