Absolute geometry and concurence of medians

Question

I'm trying with a friend to find ....the simplest proof that in absolute(neutral) geometry the medians concur. In Bachmann's book (in German-Aufbau der Geoemtrie aus Spiegelungsbegriff) there is a proof with symmetries(Hjemslev), but difficult enough. Also, we have seen a proof , which uses the whole Hilbert system for absolute geometry in space. But we have not met any ('synthetic') proof based on the axioms for the plane. If you have seen any other proof to this theorem, I'd appreciate to give us here some link or help. Thank you in advance !