(** 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 bet_cong_onc3_cases : forall O P A X Y T,
T <> O -> Bet A O T -> Cong T X T Y ->
OnCircle A O P  -> OnCircle X O P  -> OnCircle Y O P ->
X = Y \/ ReflectL X Y O A.