(** another statement for nine point circle theorem *)

Lemma l_3_45 : forall A B C E F G A1 B1 C1 r,
is_midpoint E A C ->
on_perp_d B1 E A r ->
is_midpoint F B C ->
on_perp_d A1 F C r ->
is_midpoint G A B ->
on_perp_d C1 G B (0-r) ->
parallel A1 C1 C B1.