Does a CDN deliver a cached copy of the encrypted pages?

I don't think so.

First of all, and if I don't make mistake, the encryption is different from one client to another. Clients do not handle the same cipher suite necessarily.

That was my thinking too - but there must be a way that you can use a CDN with a secure site. Otherwise CDN would be becoming obsolete instead of gaining traction.

Technically, the pages themselves aren't encrypted. Only the data traveling across the wire is. It's just like your browser's cache: a file may be downloaded to it securely via HTTPS, but it will be stored in cache in its original form. Browse your cache and you'll only find original files.

Multiple servers can serve the same or even different certificates for the same domain, but usually your server and the CDN serve requests from different domains. For example, your CDN will listen on www.example.com (publicly available), and your own server on source.example.com (privately available for the CDN). If the CDN receives a request on www.example.com for a file it doesn't (or is not allowed to) have cached, it will connect to source.example.com to pull the file (connection A: CDN <-> your server), then store it in its cache (again, if allowed) and forward it to the user (connection B: user <-> CDN). This is the same principle for HTTP and HTTPS, but both domains obviously require a valid certificate if you want both connections to be secured over HTTPS. In the end, though, the files themselves don't change from one server to the other.