## LENGTH OF PORTION OF EULER LINE INSIDE A TRIANGLE

**by Kavan Prajapati**Category: STEM

**Abstract**– The Euler line which was discovered in 1763 by Swiss mathematician Leonhard Euler, is a line that goes through the orthocenter, the centroid and the circumcenter of a non-equilateral triangle. Moreover, the distance between the orthocenter and the centroid is always double the distance between the centroid and circumcenter. This paper aims at finding the length of segment of Euler line that lies inside of a non-right scalene triangle if the length of its three sides are given. This papers aims at deriving two approaches to find the length of portion of Euler line that lies inside of a scalene non-right triangle. As a result of the approaches, this papers contributes by providing formulas that can be used for any scalene non-right triangle.