Simson's Theorem

Simson:=proc() local O, t,i,P,R:

for i from 1 to 4 do   P[i]:=ParamCircle(O,R,t[i]):   od:

Colinear(
Ft(   P[4]   ,   Le(P[1],P[2])   ),
Ft(   P[4]   ,   Le(P[2],P[3])   ),
Ft(   P[4]   ,   Le(P[3],P[1])   )
               ):

end: