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The Bevel Start End does not work on closed curves.

I need to partially bevel a profile on a circle. The circle curve added by Add->Curve->Circle is closed.

Duplicating a vertex and manually re-building an open circle results in a numerically inprecise curve.

How can I open the Circle curve without loosing a segment and end up with a mathematically exact circle?

Thanks

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Either Blender is rather non-intuitive, or I'm missing something obvious.
The fastest way I found:

  1. Add a bezier circle and make it non-cyclic (Alt + C)
  2. Rotate the end vertices to form a 3/4 circle
  3. Extrude one of the ends and complete the circle

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