(** Euclid Book III Prop 14 Equal straight lines in a circle are equally distant from the center, and those which are equally distant from the center equal one another. *)

(* Specifications: *)
Lemma cong_chord_cong_center : forall O P A B C D M N,
OnCircle A O P ->
OnCircle B O P ->
OnCircle C O P ->
OnCircle D O P ->
Midpoint M A B ->
Midpoint N C D ->
Cong A B C D ->
Cong O N O M.
(** variant *)
Lemma cong_chord_cong_center1 : forall O P A B C D M N,
A <> B -> C <> D -> M <> A -> N <> C ->
OnCircle A O P ->
OnCircle B O P ->
OnCircle C O P ->
OnCircle D O P ->
Col M A B ->
Col N C D ->
Per O M A ->
Per O N C ->
Cong A B C D ->
Cong O N O M.