(** Two circles are equal if and only if they have the same center and the same radius *)

(** Two circles are distinct if and only if there is a point belonging to the first and not to the second *)
Lemma nEqC_chara : forall A B C D, A <> B ->
~ EqC A B C D <->
(exists X, OnCircle X A B /\ ~ OnCircle X C D).