(** * Proposition 3 If in a circle a straight line passing through the center bisects a straight line not passing through the center, it also cuts it at right angles; and if it cut it at right angles, it also bisects it. *)

(* Specifications: *)
Lemma prop_3_1 : forall O P A B X,
O <> X -> A <> B ->
OnCircle A O P ->
OnCircle B O P ->
Midpoint X A B ->
Perp O X A B.
Lemma prop_3_2 : 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.