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I want to draw a single circle which includes all points in a layer, but is as small as possible (so the two outermost points are exactly at the line). Is there any way to do this in QGIS (3.4) or with a QGIS plugin?

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Use the minimum bounding geometry tool in the Procesing Toolbox. Choose the geometry type: "Minimum enclosing circle"

Note that some vector layer formats don't support circles. The circle layer will be converted to a nearly-circular polygon if you save it one of those formats.

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