(** Euclid Book III Prop 4. If in a circle two straight lines which do not pass through the center cut one another, then they do not bisect one another. *)

Lemma mid2_onc4__eq : forall O P A B C D X, B <> C-> A <> B ->
OnCircle A O P ->
OnCircle B O P ->
OnCircle C O P ->
OnCircle D O P ->
Midpoint X A C ->
Midpoint X B D ->
X=O.