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. *)
(** Every point on the tangent different from the point of tangency is strictly outside the circle. *)

Lemma tangent_out : forall A B O P T X,
X <> T -> Col A B X -> TangentAt A B O P T -> OutCircleS X O P.