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 onc3_mid2__ncol : forall O P A B C A' B',
O <> P ->
OnCircle A O P -> OnCircle B O P -> OnCircle C O P ->
Midpoint A' A C -> Midpoint B' B C -> ~ Col A B C ->
~ Col O A' B' \/ A' = O \/ B' = O.