Section Tangency.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** Euclid Book III, Prop 11 and Prop 12 We do not need to distinguish between internal or external tangency. *)
(** If two circles are tangent, the common point is on the line joining the centers. *)
(** A line going through the center is not tangent to the circle. *)

Lemma diam_not_tangent : forall O P A B,
P <> O -> Col O A B -> ~ Tangent A B O P.