more about 6 mid-points
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?
(This is an extended version of another activity with additional objects here to facilitate investigation. You may also check the video below for sharing of my thoughts on this problem.)