Fregier's Theorem

Fregier:=proc()local O,d,t0,t1,s1,t2,s2,P0,P1,P2,Q0,Q1,Q2,X1,X2:

P0:=ParEllipse(O,d,t0):
P1:=ParEllipse(O,d,t1):   P2:=ParEllipse(O,d,t2):   Q1:=ParEllipse(O,d,s1):  Q2:=ParEllipse(O,d,s2):

P2:=subs(t2=solve(Slope(P0,P1)*Slope(P0,P2)=-1,t2),P2):
Q2:=subs(s2=solve(Slope(P0,Q1)*Slope(P0,Q2)=-1,s2),Q2): 

Concurrent(NormalToEllipse(O,d,t0),Le(P1,P2),Le(Q1,Q2)):

end: