(** 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 onc2_mid_cong_col : forall O P U V M X,
U <> V ->OnCircle U O P -> OnCircle V O P -> Midpoint M U V -> Cong U X V X -> Col O X M.