(** 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 cong2_onc3__eq : forall O P X A B C, A <> B -> A <> C -> B <> C ->
OnCircle A O P -> OnCircle B O P -> OnCircle C O P ->
Cong X A X B -> Cong X A X C ->
X = O.