Section Inscribed_angle.
Context `{TE:Tarski_euclidean}.
(** The sum of the angles of a triangle is the flat angle. *)
(** If A, B and C are points on a circle where the line AB is a diameter of the circle, then the angle ACB is a right angle. *)
(** In a right triangle, the midpoint of the hypotenuse is the circumcenter. *)
(** If the angle ACB is inscribed in a circle of center O and C, O lie on the same side of AB, then this angle is acute. *)
(** Euclid Book III Prop 20: In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base. *)
(** In a circle the angle at the centre is double of the angle at the circumference. *)
(** If two angles ACB and ADB are inscribed in the same circle, then they are either congruent or supplementary. *)

Lemma cop2_onc4__or_conga_suppa : forall O P A B C C',
A <> B -> B <> C -> A <> C -> B <> C' -> A <> C' ->
OnCircle A O P -> OnCircle B O P -> OnCircle C O P -> OnCircle C' O P ->
Coplanar A B C O -> Coplanar A B C' O ->
CongA A C B A C' B \/ SuppA A C B A C' B.