I have a 200 mile diameter circle in Google Earth. 
I saved as a kml and imported into QGIS with the "add vector layer" and it was imported as WGS 84 GCS. 
Now the Circle lines up on the correct coordinates but is an oval and measures east to west well over 270 miles however 200 north to south. Why do the Coordinates match but not the distance measurements? Does one program not account for curvature and the other not? What coordinate system do you use from google earth to Qgis to be able to maintain a circle a 200 mile diameter?
Answer
Use the CRS EPSG:3857. See below.
Circle in GE 
Same KML as WGS 84 in QGIS 
Same KML again using EPSG:3857 
Measure the diameter of your circle and it should be much better.
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