(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
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Require Export area_method.
(* A small lemma to check that centroid is really at the intersection of medians. *)

Lemma l6_47 : forall A B C G M N,
is_centroid G A B C ->
on_line M A B ->
inter_ll N G M A C ->
parallel M B A M -> A<>M -> A<>N ->
parallel N C A N -> B<>M ->
1+2<> 0 -> 2+1 <> 0 ->
M**B/A**M + N**C/A**N = 1.