(** 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. *)

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.