Definition Tcircle : Type := Tpoint*Tpoint*Tpoint %type.Definition OnCirc P (C:Tcircle) := 
  match C with 
  (X,A,B) => tarski_axioms.Cong X P A B
  end.Definition CI (J:Tcircle) A C D := J=(A,C,D) /\ C<>D.Definition InCirc P (J:Tcircle) :=
   match J with
  (C,A,B) => 
   exists X Y, Definitions.BetS X C Y /\ tarski_axioms.Cong C Y A B /\
               tarski_axioms.Cong C X A B /\ Definitions.BetS X P Y
  end.Definition OutCirc P (J:Tcircle) :=
   match J with
  (C,A,B) => 
      exists X, Definitions.BetS C X P /\ tarski_axioms.Cong C X A B
 end.

Lemma circle_line : circle_circle -> forall A B C K P Q, CI K C P Q -> InCirc B K -> A <> B -> exists X Y, Definitions.Col A B X /\ Definitions.Col A B Y /\ OnCirc X K /\ OnCirc Y K /\ Definitions.BetS X B Y.