### 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

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## Cite this

Harutyunyan, D., Nazaryan, A., & Pambuccian, V. (2019). The Hajja–Martini inequality in a weak absolute geometry.

*Journal of Geometry*,*110*(2), [24]. https://doi.org/10.1007/s00022-019-0481-3