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The Geometer's Sketchpad
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By moving the vertices of the gray quadrilateral, you can change where the internal circle is placed. (It is defined by the midpoints of the sides.) By moving point D around, you can see that any point on the outer circle can be the vertex of an inscribed quadrilateral with midpoints of edges on the same second circle. This porism was inspired by a
from Steve Gray. It seems to be true for higher order n-gons, but I have only proved it for n = 3 and 4.
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