Section ABC.
Variable A B C : Tpoint.
Definition isosceles A B C :=
Cong A B B C.
(** In a triangle isosceles in A the altitude wrt. A, is also the bisector and median. *)

Lemma isosceles_foot__midpoint_conga :
forall H,
isosceles A B C ->
Col H A C ->
Perp H B A C ->
~ Col A B C /\ A<>H /\ C<>H /\ Midpoint H A C /\ CongA H B A H B C.