How are websites aware that you are using Tor to connect to them. I thought the Ip addresses of the computers through which you are routed, were indistinguashible from the rest and thus helped you be anonymous online.
No, you share a network of nodes operated by volunteers. Since all Tor users can use any node and hence any exit IP, your indistinguishable* from other Tor users. Tor does in no way try to hide the fact that you're using Tor. The ability for the client to pick an arbitrary exit relay (and thereby any IP in the pool) is part of the security design, you don't want anyone else to be able to decide what path your traffic takes through the network. However, as a direct consequence, it's very easy to enumerate the IP addresses of all nodes in the network. Matter of fact, you can get a list of all IPs used by Tor exit nodes online. Trying to hide the IPs would be futile, with the possibility to use any exit, you could simply go through all of them and observer the IP address.
* By indistinguishable, I'm talking about your IP address, your behavior may still allow to identify you (e.g. using the same search term all the time, logging in, use of a particular browser, …).