proposition: Lemma centroid_theorem : forall A B C A1 B1 C1 G, Midpoint A1 B C -> Midpoint B1 A C -> Midpoint C1 A B -> Col A A1 G -> Col B B1 G -> Col C C1 G \/ Col A B C.
proof: Proof. intros A B C A1 B1 C1 G; convert_to_algebra; decompose_coordinates. intros; spliter. express_disj_as_a_single_poly; nsatz. Qed.
imports: Description Ring Field Nsatz Rtauto GeoCoq.Tarski_dev.Ch16_coordinates GeoCoq.Tarski_dev.Ch15_pyth_rel GeoCoq.Tarski_dev.Annexes.midpoint_theorems