Midpoint of a segment with only circles
Source: flanders '05
September 28, 2005
ratiosymmetrygeometrycongruent triangles
Problem Statement
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 is the midpoint of .
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