It is not quite as simple as that: with basic text it is possible, if you use a WebBrowser control and set the DocumentText property to the string - there are problems though if you use any relative paths (including those starting "~").
The only other way is to save the file each time the RTB changes, and tell the browser to refresh: the easiest way is to send the F5 key to the browser - there is an article here which may help:
Sending Keystrokes to another Application in C#[
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