(** If a line passing through the center of a circle is perpendicular to a chord, then they intersect at the middle of the chord *)

(* Specifications: *)
Lemma col_onc2_perp__mid : forall O P A B X,
O<>X -> A<>B -> Col A B X -> OnCircle A O P -> OnCircle B O P -> Perp O X A B -> Midpoint X A B.