Miquel's Five Circle Theorem

MiquelFiveCircle:=proc() local s,P,Q,Qa,gu,i,r,C:

s[5]:=-1/mul(s[i],i=1..4):
gu:=1:
for i from 1 to 5 do
P[i]:=ParamCircle([0,0],1,gu):
Q[i]:=ParamCircle([0,0],1,gu*s[i]):
r[i]:=expand(DeSq(P[i],Q[i])):
C[i]:=expand(DeSq([x,y],P[i])-r[i]):
gu:=gu*s[i]*s[i+1]:
od:
for i from 1 to 4 do
Qa[i]:=OtherCeCe(C[i],C[i+1],Q[i]):
od:
evalb(normal( DeSq (Pt (Le (Qa[1],Qa[2]), Le(Qa[3],Qa[4])),P[3])- DeSq (Q[2],P[3]))=0):
end: