Sum of the squares of the distances to the vertices

Minimizing sums of the squares of the distances
Try to locate the position of the point that will minimize the sum of the squares of distances from that point to the three vertices of a triangle. Once you have the approximate location, press at the box to show extensions and intersections. What can you say about the position of points E, F, and G? State a conjecture about the location of the point that minimizes the squares of distances based on your previous observation.