Reconstructing a circle from an arc. Best method?

Inherited a project from another designer. Trying to find the center point of an arc's original circle to add some radial elments to it.
Any clever/easy ways to reconstruct the original circle (other than eyeballing it)?

Assuming the arc is a single open path:
1. Line Tool: ShiftDrag to draw a short vertical line. Black stroke, no fill.
2. AltShiftDrag a copy of it a short distance rightward.
3. Select both. Drag & Drop into Brushes Palette. Define an Artbrush.
4. Select the arc. Copy. Apply the Artbrush.
5. Increase Stroke weight until the two lines cross.
6. Expand Appearance.
Assuming the arc is a closed path like in your example:
First, directSelect the segment(s) that make up one curved side of the shape. Copy. PasteInFront. Then proceed as described above.
JET

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