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 prop_7_8 : forall O P A B T X Y , Diam A B O P -> Bet A O T
-> OnCircle X O P -> OnCircle Y O P
-> LeA A O X A O Y -> Le T Y T X.