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.

(* Specifications: *)
Lemma altitude_intersect:
forall A  A1 B B1 C C1 O: Tpoint,
~ Col A B C ->
Perp A A1 B C  -> Perp B B1 A C -> Perp C C1 A B ->
Col O A A1 -> Col O B B1 ->
Col O C C1.