Require Export GeoCoq.Elements.OriginalProofs.proposition_10.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ABCequalsCBA.
Require Export GeoCoq.Elements.OriginalProofs.lemma_equalanglestransitive.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_09 :
forall A B C,
nCol B A C ->
exists X, CongA B A X X A C /\ InAngle B A C X.