How to set the global search center for a farm to serve both the intranet and extranet sites?

What is the proper value for a global search center url when there are intranet and extranet urls in use?

Consider a farm with a search center configured at the following url:

 http://intranet/sites/search

 And, assume that there are several other web applications in use, and anyone on the farm who selects to search “everything” should be redirected to the above site.

So, set the global search center url to http://intranet/sites/search/pages?

To complicate it further, assume there is a separate URL used by external users(http://extranet.company.com), and that external users cannot access http://intranet. So, a user goes to http://extranet.company.com, they type something in the search box, select to search everything, and the system then tries to redirect them to http://intranet/sites/search/pages, which they can’t access.

 So, instead of http://intranet/sites/search/pages, perhaps a relative url: /sites/search/pages? But, there are multiple web apps, and so if a user is browsing http://otherwebapp and searches, they will be redirected to http://otherwebapp/sites/search, which doesn’t exist.

 Thoughts?

Mike G.