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How can I trust all my Tor nodes in path


I have read in the Tor documentation that the number of Tor routers in a path is hard-coded at 3.  And I understand that the path changes every 10 minutes (except for active connections).

As a client not running a server, how am I sure that at least one of the nodes in the path can be trusted?

A little math:  assume there are 200 Tor routers, some of which have been compromised and owned by the same attacker.  If the number compromised is small, I can be somewhat confident that at least one router is trusted.  However, suppose the attacker massed a "global attack" on the Tor network:  all at once the attacker introduces 10,000 new routers into the network, all of which he has control of.  Now, when I choose 3 routers for my path, I only have a few that may be trusted, which are in the original 200.

Has this problem been addressed elsewhere?

Thank you in advance.

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