Finagling a Nagel Point in Taxicab Geometry and Beyond

We discuss two possible ways to define Nagel points for triangles when using the taxicab distance formula. The two approaches are equivalent in Euclidean geometry since a triangle's extouch points divide the triangle's perimeter in half, but this is not the case with the taxicab distance formula. We will discuss how using extouch points does not always lead to a unique taxicab Nagel point, but using points that split the perimeter does. In fact, we show that the most common proof for the existence of the Euclidean Nagel point and its Barycentric coordinates holds when replacing the Euclidean distance formula with any lp‐metric.