(** Given a circle, there is a point strictly outside the circle. *)

(** Given a circle of center O and a line OX, O is between two points of the line which are also on the circle. *)
Lemma diam_points : forall O P X, exists Q1 Q2,
Bet Q1 O Q2 /\ Col Q1 Q2 X /\ OnCircle Q1 O P /\ OnCircle Q2 O P.