The leading edge
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Radius is from the center of a circle to the outer edge. Diameter is from the outer edge to the opposite outer edge, i.e., through the center. The diameter has twice the length of the radius.
A helicoid. The outer edge is a helix but since it is a plane, not a line, it becomes a helicoid.
be worn open
No, it is the outer edge of the circle; the rim; the perimeter
a circle