(** AB is tangent to the circle (O,P) iff they intersect at a point X such that AB is perpendicular to OX. *)

Lemma tangency_chara3 : forall A B O P Q, A <> B ->
OnCircle Q O P -> Col Q A B ->
((forall X, Col A B X -> OutCircle X O P) <-> Tangent A B O P).