The Minnesota Journal of Undergraduate Mathematics
The Euler line of a triangle passes through several important points, including three specific triangle centers: the centroid, orthocenter, and circumcenter. Each of these centers is the intersection of lines related to the triangle, mainly its medians, altitudes, and perpendicular bisectors, respectively. We present three theorems which initially share a similar construction. Each involves starting with a triangle and a point. After connecting the triangle’s vertices to that point, creating additional triangles, we establish connections to either the centroids, orthocenters, or circumcenters of the new triangles.
Lezark, K., Capaldi, M. (2016). New findings in old geometry: Using triangle centers to create similar or congruent triangles. The Minnesota Journal of Undergraduate Mathematics, 2(1).