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

(* Specifications: *)
Lemma EqC_chara: forall A B C D, EqC A B C D <-> A = C /\ Cong A B C D.
(** 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).
Lemma EqC_sym : forall A B C D, EqC A B C D -> EqC C D A B.
End Circle_2.