# On the Erdos-Mordell Inequality for Triangles in Taxicab Geometry

## TL;DR

This paper investigates the Erdos-Mordell inequality within taxicab geometry, establishing conditions under which the inequality holds with a specific weight factor, expanding geometric inequalities into non-Euclidean contexts.

## Contribution

It extends the Erdos-Mordell inequality to taxicab geometry, identifying the conditions and a specific weight factor where the inequality remains valid.

## Key findings

- The inequality holds for certain triangle configurations in taxicab geometry.
- The weight factor w = 3/2 ensures the inequality's validity.
- Conditions on points A, B, C are specified for the inequality to hold.

## Abstract

In this work the Erdos-Mordell's inequality is examined for the case of a triangle $ABC$ in the taxicab plane geometry. It is shown that the Erdos-Mordell's inequality $R_A + R_B + R_C \, \geq \, w \, (r_a + r_b + r_c)$ holds for triangles with appropriate positions for its points $A$, $B$ and $C$, if $w = 3/2$.