Generate an ICredentials object from HttpContext.Current

I have a Solution with two Web Applications.  A page (pageA) in Web Applications A needs to display the content from a page (pageB) in Web Application B.  I set up this up as so:

public class pageA : System.Web.UI.Page
{
protected override Page_Load(object sender,EventArgs e)
{
System.Net.WebClient client = new WebClient();
Stream htmlStream = client.OpenRead("http://localhost/WebApplicationB/pageB.aspx");
Response.Write(new StreamReader(htmlStream).ReadToEnd());
}
}

Everything works fine if WebApplicationB is set up in IIS for anonymous access.  However, I need to set up the site to use Basic Authentication.  When WebApplicationB requires authentication, my code above will throw a WebException saying a 401 unauthorized HTML status code was returned.  This is to be expected as my WebClient object isn't passing any credentials.

If I modify the code as so:
System.Net.WebClient client = new WebClient();
client.Credentials = new NetworkCredential("validUserName","validPassword");

Everything is happy again.  

However, I don't want to hard code a username / password and I don't want to store it in a web.config or other settings file.  Since my WebApplicationA is using the same authentication as WebApplicationB is there a way to get the Identity of the user making the request to WebApplicatioA\PageA and use that to build a NetworkCrendential or ICredentials object?  

In other words,

System.Net.WebClient client = new WebClient();
client.Credentials = (NetworkCredential)HttpContext.Current.Request.User;

Thanks,

PJ