another problem, slightly extended, from aplusclick

a semicircle is inscribed in a right angled triangle with sides ( a , b, c )

what is the radius of this semicircle if

( a , b , c ) =

1) ( 6 , 8 , 10 )

2) ( 15 , 36 , 39 )

3) ( 28 , 96 , 100 )

what patterns are there in these triples and the resulting radius?

what would the next few be?

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