Your aspx page is using Verdana font by default.
You didn't use the Editor.EditorWysiwygModeCss Property specify the location of the style sheet that will be used by the editable area.
1. When I load the editor it starts off as Verdana.
The editor detects the aspx page is using Verdana font.
2. As soon as I click into the text area it changes to Times New Roman.
The editor gets focus. And can't find any default font specified in your style sheet, so it show the window default font (Times New Roman).
3. If I click back outside of the text area it changes back to verdana.
Same as 1.
4. If I come back to the text area back to TNR again.
Same as 2.
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