(** The points on the bisector of an angle are at equal distances of the two sides. *)

Lemma bisector_perp_equality : forall A B C I H1 H2, Coplanar A B C I ->
Col B H1 A -> Col B H2 C ->
Perp A B I H1 -> Perp B C I H2 ->
CongA A B I I B C ->  Cong I H1 I H2.