trapped semicircle

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?