Fuhrmann's Theorem

Fuhrmann:=proc() local O,r P,Q,R,L,M,N,a,b,c,a1,b1,c1,e,f,g,t2,t3,t4,t5,t6,A,B,gu:

P:=ParamCircle(O,r,t1):   Q:=ParamCircle(O,r,t2):   R:=ParamCircle(O,r,t3):
L:=ParamCircle(O,r,t4):   M:=ParamCircle(O,r,t5):   N:=ParamCircle(O,r,t6):  
a:=DeSq(L,M):   b:=DeSq(R,Q):   c:=DeSq(N,P):
a1:=DeSq(P,Q):   b1:=DeSq(M,N):   c1:=DeSq(L,R):
e:=DeSq(R,N):   f:=DeSq(L,P):   g:=DeSq(M,Q):
SumSqRtsIsZero([a*a1*e,b*b1*f,c*c1*g,a*b*c,a1*b1*c1,e*f*g]):

end: