Creates a new object offset a specific distance from an original.
Controls how the offset curve will connect breaks caused by corners in the original curve. This option does not apply to surface offsets.
Off: Do not connect the break. Note that this option can create two or more separate new curves.
Linear: Connect the break with tangential lines.
Circular: Connect the break with an arc.

tool or degree 1 curves.
In both of these cases, the result is like linear.
Active View: the copy is offset in the plane of the active view. For example, in Z-up environment, the Top view would offset in the XY plane.
Geometry Average: the copy is offset in the average plane of the curve. Planar curves will be offset in the curve’s plane, 3D curves will be offset in 3D.
The distance between the original and the offset copy.
Remove loops caused by concave angles in the original curve.
Curve Loop Cutting creates multi-knots, which can cause problems for some surface creation tools such as Rail Surface.

to change the curve cutting
radius while using the tool.
Set this value greater than 0 to create a smooth arc with the given radius where the Offset tool cuts loops, instead of a corner.

The maximum number of times the offset geometry will be subdivided for more accurate approximation of the original. The default is 5 (each span of the original can be represented by up to 5 spans on the offset copy).
If you do not mind extra edit points (a more complex curve), you can increase this number for a more accurate offset copy of complex geometry.
This option is only available when Explicit control is on.
Automatically updates the object as you change options in the window.
Gives you control over the number of extra spans the tool will insert in the offset surface.
Link the offset object to the original through construction history, so changes to the original affect the offset object.
Create curves-on-surface on the offset surface to match any curves on surface on the original.
When Create History is on, the curves-on-surface on the offset surface are linked to the curves-on-surface on the original.