proposition: Lemma altitude_is_perp_bisect : forall A B C O A1 E F, A <> O -> E <> F -> Perp A A1 B C -> Col O A1 A -> Col A E F -> Par B C A E -> Midpoint A E F -> Perp_bisect A O E F.
proof: Proof. Proof with finish. intros. apply perp_mid_perp_bisect... apply perp_sym. apply cop_par_perp__perp with B C... apply par_col_par with A... apply perp_col1 with A1... Qed.
imports: GeoCoq.Highschool.circumcenter