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. *)

(* Specifications: *)
Lemma TangentCC_Col : forall A B C D X,
TangentCC A B C D ->
OnCircle X A B ->
OnCircle X C D ->
Col X A C.
Lemma tangent_neq : forall A B O P,
O<>P -> Tangent A B O P -> A<>B.