An Extending Classical Problem in Geometry

Abstract

In geometry, there is a classic theorem states that the sum of the distances from any point in the interior of an equilateral triangle to each of the sides of the triangle is a constant. This theorem has received many interests and been widely studied, resulting in other lemmas and theorems extended from this classic theorem. In this paper, we analyze and discuss a lemma and a theorem about the calculation of the sum of such distances for any triangle and regular polygon.