(** Euclid Book III Prop 9. If a point is taken within a circle, and more than two equal straight lines fall from the point on the circle, then the point taken is the center of the circle. *)

Lemma Prop_7_8_uniqueness : forall O P A X Y Z T, T <> O -> X <> Y ->
Bet A O T -> Cong T X T Y -> Cong T X T Z ->
OnCircle A O P -> OnCircle X O P -> OnCircle Y O P -> OnCircle Z O P ->
Z = X \/ Z = Y.