(** If a point is inside a circle, then it lies on a radius. *)

(* Specifications: *)
Lemma inc__radius : forall O P X, InCircle X O P ->
exists Y, OnCircle Y O P /\ Bet O X Y.
Lemma onc_not_center : forall O P A, O <> P -> OnCircle A O P -> A <> O.
Lemma onc2_per__mid : forall O P U V M, U <> V -> M <> U ->
OnCircle U O P -> OnCircle V O P -> Col M U V -> Per O M U -> Midpoint M U V .