Based on your screen shots, I came up with a couple of points in your circle.
Suppose we have the central coordinate lat: 48.853647, lon: 2.347894 and a point in lat: 48.853647 lon: 2.32 (a point on the same lat, but further west):
Using distance_type: plane the estimated distance is ~ 3.1km, while using distance_type: arc the distance is ~ 2 km.
If we use another point, lat: 48.8717 lon: 2.347894 (further north of the central point, but some lon) using distance_type: plane, distance ~ 2 km and using distance_type: arc is ~ 2 km.
Therefore, if the filtered distance is say 2.5 km, then using the distance_type: arc parameter will correctly include both points using the distance_type plane: the plane will include only the north point giving an elliptical shape.
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