Hello! I'm having trouble with my proof.

Definitions:

Centroid of a triangle ABC: G

Orthocentre of a triangle ABC: H

Circumference of a triangle ABC (circle passes though the vertices, A, B, C): O

Question: Prove that G, H and O of any triangle lie on any line.

Proofs are my Achilles heel. So far the only progress I have made is:

Any help would begreatlyappreciated.