proposition: Lemma cong2_onc3__eq : forall O P X A B C, A <> B -> A <> C -> B <> C -> OnCircle A O P -> OnCircle B O P -> OnCircle C O P -> Cong X A X B -> Cong X A X C -> X = O.
proof: Proof. intros O P X A B C HAB HAC HBC HAOn HBOn HCOn HCong1 HCong2. assert (HCop := all_coplanar A B C O). assert (HCop1 := all_coplanar A B C X). apply cong2_cop2_onc3__eq with P A B C; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel