Intriguing invariants of centers of ellipse-inscribed triangles. (English) Zbl 1477.51008
In this paper, the authors describe intriguing properties of a 1d family of triangles: two vertices are pinned to the boundary of an ellipse while a third one sweeps it. They prove that: (i) if a triangle center is a fixed affine combination of barycenter and orthocenter, its locus is an ellipse; (ii) over the family of said affine combinations, the centers of said loci sweep a line; (iii) over the family of parallel fixed vertices, said loci rigidly translate along a second line.
Reviewer: Cătălin Barbu (Bačau)
MSC:
| 51M04 | Elementary problems in Euclidean geometries |
| 51N20 | Euclidean analytic geometry |
| 53A04 | Curves in Euclidean and related spaces |
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