clear all
; Some more fun formulas.  These are very similar to Heron's formula
; for the area of a triangle (see "heron.in").

s=.5*(a+b+c)
; radius of a circle inscribed in a triangle with sides of length (a, b, c):
r=(s*(s-a)*(s-b)*(s-c))^.5/s
elim s using 1
unfactor
simp
; radius of a circle circumscribing a triangle with sides of length (a, b, c):
r=a*b*c/(4*(s*(s-a)*(s-b)*(s-c))^.5)
elim s using 1
simp