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(* 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_44 : forall A B C G P Q,
is_centroid G A B C ->
on_inter_line_parallel P G A B B C  ->
on_inter_line_parallel Q G A C B C  ->
G<>Q -> G<>P -> 1+2 <> 0 ->
2*2*S4 P Q C B = (2+2+1)* S A Q P.