Section Circle_2D.
Context `{T2D:Tarski_2D}.
(** The center of a circle belongs to the perpendicular bisector of each chord *)
(** Euclid Book III Prop 4. If in a circle two straight lines which do not pass through the center cut one another, then they do not bisect one another. *)
(** Euclid Book III Prop 9. If a point is taken within a circle, and more than two equal straight lines fall from the point on the circle, then the point taken is the center of the circle. *)

Lemma onc2_mid_cong_col : forall O P U V M X,
U <> V ->OnCircle U O P -> OnCircle V O P -> Midpoint M U V -> Cong U X V X -> Col O X M.