Section Concyclic.
Context `{TE:Tarski_euclidean}.
Definition Concyclic A B C D := Coplanar A B C D /\ exists O, Cong O A O B /\ Cong O A O C /\ Cong O A O D.

Lemma concyclic_trans : forall A B C D E,
~ Col A B C ->
Concyclic A B C D  -> Concyclic A B C E -> Concyclic A B D E.