The Euler line of a triangle
The Euler Line of a triangle is simply a straight line that passes through four of the commonly known centers of the triangle. They are, Circumcenter(C) Centroid(G) Orthocenter(H) Nine-point center(L) It creates more of an impact if we say it the other way around. That is, for any given triangle the above mentioned four centers are always collinear; they lie on the same line - the Euler Line. Things are slightly different for an equilateral triangle. These four centers are the same single point. We can draw infinitely many lines passing through a single point. And so it only makes sense that the concept of 'the' Euler line is associated only with non-equilateral triangles. Now for those of you reading this who don't know about these four centers of a triangle, let me quickly give a short description of each one of them. Circumcenter is the center of the circumcircle of a triangle. It is the circle through the three vertices of the triangle. Circumcen...