6 mid-points

Arthur Lee
Given 4 points, A,B,C,D, we can form 6 pairs of points. Each pair of points gives one line and one mid-point. This figure shows the 6 mid-points in orange. How would you arrange the 4 points (A to D), so that the 6 mid-points all lie on one circle? Try to find a more general condition. What do you notice when trying to do so or explain your findings? (You may find an extended version of this activity with more suggestions if you prefer.)