(** The points which are at equal distance of the two side of an angle are on the bisector. *)

Lemma perp_equality_bisector : forall A B C I H1 H2,  ~ Col A B C ->
InAngle I A B C -> Col B H1 A ->
Col B H2 C -> Perp A B I H1 -> Perp B C I H2 -> Cong I H1 I H2 ->
CongA A B I I B C.