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. *)
(** 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 onc4_cong2__eq:
forall A B C D O P X,
A<>B -> C<>D ->
~ Par A B C D ->
OnCircle A O P ->
OnCircle B O P ->
OnCircle C O P ->
OnCircle D O P ->
Cong A X B X ->
Cong C X D X ->
O=X.