Section circle_continuity.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

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.