Some Homothetic Triangles Related to the Euler Line

Abstract

In this note the triangle formed by the tangents to the circumcircle at the vertices of a given triangle is called the circumtriangle of the given triangle; the triangle formed by the points of contact of the incircle with the sides of a given triangle is called the intriangle of the given triangle; and the triangle formed by the points of contact of an excircle with the sides of a given triangle is called an extriangle of the given triangle.