Section Circumcenter.
Context `{TE:Tarski_euclidean}.
Definition is_circumcenter G A B C := Cong A G B G /\ Cong B G C G /\ Coplanar G A B C.

Lemma is_circumcenter_perm : forall A B C G,
is_circumcenter G A B C ->
is_circumcenter G A B C /\ is_circumcenter G A C B /\
is_circumcenter G B A C /\ is_circumcenter G B C A /\
is_circumcenter G C A B /\ is_circumcenter G C B A.