Giving a general triangle constant width

Start with three points A, B and C. Join then with indefinite lines.
Add a point on AB, not between these points.
Draw a circular arc, centred at A, through D. Mark E where this intersects AC.
Draw a circular arc, centred at C, through E. Mark where this intersects BC.
Draw a circular arc, cantred at B through this point.

Complete the shape back to D.

There is a natural feasibility constraint, forcing D to be sufficiently far from A. Move D to see what happens.

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Chris Sangwin, 9 Feb 2007, Created with GeoGebra