Homebrew doesn't find XCode 4.3

When I try to install something with homebrew I get an error message that it does not find XCode. But I just installed XCode 4.3 and also did a reboot.

admins-MacBook-Pro-2:~ ernst$ brew install macvim
Warning: Xcode is not installed! Builds may fail!
Error: No such file or directory - /usr/bin/cc
admins-MacBook-Pro-2:~ ernst$ 

Any ideas?

Update:

admins-MacBook-Pro-2:~ ernst$ which cc
admins-MacBook-Pro-2:~ ernst$ echo $PATH
/usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin:/usr/X11/bin
admins-MacBook-Pro-2:~ ernst$ 

I had the same problem and found the solution in Homebrew's issues page. Open Xcode, open Preferences, select Downloads, and install Command Line Tools. Once it is installed Homebrew should work.