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

Lemma prop_9 : 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.