Euler's Discovery
In this dynamic worksheet, create an arbitrary triangle ABC using the polygon tool. Then using the custom tools with the Icon wrench use the dropdown to select and follow the instructions for using the tools of Circumcentre. The point D formed and is the circumcentre of the triangle. Using the tool icon circle with centre create a circle with centre D through one of the vertices of triangle ABC. Point E is formed using the Orthocentre tool and point F is formed using Centroid tool. Three distinct points will appear and form on the function of a line. Use the line tool to connect any two points of these three. That line is called the Euler line. When the triangle formed is an equilateral triangle the Euler line is undefined since the circumcentre, orthocentre and centroid exist at the one point. Drag points A, B and C of the polygon triangle ABC to see the dynamics associated with the Euler line.