proposition: Lemma tree_points_onc_cop : forall O P, O <> P -> exists A B C, A <> B /\ A <> C /\ B <> C /\ OnCircle A O P /\ OnCircle B O P /\ OnCircle C O P /\ Coplanar A B C O.
proof: Proof. intros O P HOP. destruct (not_col_exists O P) as [X HNCol]; auto. destruct (diam_points O P X) as [B [C [HBet [HCol []]]]]. exists P, B, C. repeat split; Circle. intro; subst; apply HNCol; ColR. intro; subst; apply HNCol; ColR. intro; treat_equalities; auto. exists B; left; split; Col. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel