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Footballguy

Translated from French so I may get some terms wrong.
In triangle ABC, the height from point B cuts AC at D. Also, the height from point C cuts AB at E.
In the triangle, ADE, the height from point D cuts AE at F and the height from point E cuts AD at G.
Demonstrate the equalities: AD x AE = AB x AG = AC x AF
They are supposed to use Thales theorem without numeric values.