DoubleElementCircle[circle, 6 points]
Select the circle, and two sets of points:
A, B, C,
A', B', C'
Gives the (perspective axis) and the double elements of the projection on the circle.
Not the biggest time saver but saves some clutter.
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Steiner's Double Element Constructions
1) Double points of two ranges on a circle: [url]http://www.geogebratube.org/material/show/id/35593[/url]
2) Double rays from a point: [url]http://www.geogebratube.org/material/show/id/35600[/url]
3) Double points on a line: [url]http://www.geogebratube.org/material/show/id/35633[/url]
