Require Export GeoCoq.Highschool.midpoint_thales.
Require Export GeoCoq.Highschool.exercises.
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_cases :
forall A B C G,
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 ->
is_circumcenter G A B C.