The Euler line and the center of mass of the triangle (centroid)

Euler line
Draw the notable points (barycenter, circumcenter and orthocenter) of the same triangle ABC. Build a straight line that passes through the orthocenter and the circumcenter.
Analysis on the Euler line
Is the barycenter in the straight line that passes through the orthocenter and the circumcenter?[br]
Property of the Barycenter
Draw the centroid G of an triangle ABC. Then, draw the triangles ABG, BCG and ACG. Calculate the area of each of these triangles. What do you notice? [br]
Justify the properties
Search and give references that justify the properties seen in previous exercises. paste the links here)[br][br][br]
Close
– Jorge Cássio

Information: The Euler line and the center of mass of the triangle (centroid)