Consider two triangles Ξπ΄π΅πΆ and Ξπ΄π΅π· that have common side π΄π΅, and the circumcentre, orthocentre and centroid of both triangles. Draw a line connecting the circumcentres, a line connecting the orthocentres and a line connecting the centroids. Which of these lines are parallel to πΆπ·? You may conveniently choose coordinates for A,B,C,D, so long as Ξπ΄π΅πΆ and Ξπ΄π΅π· are not similar nor congruent.
