Require Export GeoCoq.Tarski_dev.Annexes.circles.
Require Export GeoCoq.Axioms.continuity_axioms.
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. *)

Lemma tangent_neq : forall A B O P,
O<>P -> Tangent A B O P -> A<>B.