Section InCenter.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition is_incenter I A B C :=
~ Col A B C /\ CongA B A I I A C /\ CongA A B I I B C /\ CongA A C I I C B.
(** Proof of the existence of the incenter of a triangle. *)

Lemma incenter_dec : forall A B C I, is_incenter I A B C \/ ~ is_incenter I A B C.