Starting with two points A and B, some circles and points are constructed as shown in
the figure:[*]the circle with centre A through B
[*]the circle with centre B through A
[*]the circle with centre C through A
[*]the circle with centre D through B
[*]the circle with centre E through A
[*]the circle with centre F through A
[*]the circle with centre G through A
(I think the wording is not very rigorous, you should assume intersections from the drawing)
Show that M is the midpoint of AB.
http://www.mathlinks.ro/Forum/album_pic.php?pic_id=291 ratiosymmetrygeometrycongruent triangles