Participar de olimpiadas
Moreover, is there a general rule for the use of these preposition after a verb or a book/website where I can check which preposition correspond to a given verb?
The preposition we usually use with "participar" is "en", as explained in this site.
However, "de" can also be found (according to the mentioned site, in Latin America).
Living in Argentina, I actually use both. There is a slight difference between them, in my opinion. While "participar en" is more usual for taking part in any event, "participar de" also conveys some sense of belonging, as if the person taking part were actually a member or a part of the event or group, so much so that there are instances where only "participar de" is used.
In invitations to take part in celebrations, it used to be common to find the expression: Participamos a usted de la boda / del bautismo de ... and the people taking part in those celebrations will tend to use the preposition "de" rather than the preposition "en" to indicate their personal involvement: Participé de la boda / del bautismo.
The expression "participar de" is also a somewhat formal version of the verb "compartir" (share): participar de la alegría de alguien (share sb's happiness).