Abstract
Solving a problem left open in Hajja and Martini (Mitt. Math. Ges. Hamburg 33:135–159, 2013), we prove, inside a weak plane absolute geometry, that, for every point P in the plane of a triangle ABC there exists a point Q inside or on the sides of ABC which satisfies: AQ≤AP,BQ≤BP,CQ≤CP.If P lies outside of the triangle ABC, then Q can be chosen to both lie inside the triangle ABC and such that the inequalities in (1) are strict. We will also provide an algorithm to construct such a point Q.
Original language | English (US) |
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Article number | 24 |
Journal | Journal of Geometry |
Volume | 110 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1 2019 |
Keywords
- Absolute plane geometry
- geometric inequalities
ASJC Scopus subject areas
- Geometry and Topology