The red lines show the three perpendiculars from the vertices to the opposite sides meeting in the orthocentre O, the blue lines show the three lines from the vertices to the midpoints of the opposite sides meeting in the centroid G and the green circle surrounds the triangle and the circumcentre P. These three points lie on a line with the centroid one-third of the distance between the other two points.

To manipulate this picture, click and move the points A, B and C. This applet was kindly provided by Chris Sangwin and was produced using GeoGebra.