| Consider the square enclosed in two circles, as shown here. Again, from Euclid, the line segment from the center of the square (and circles) to the midpoint of any edge is perpendicular to that edge. |
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| Consider the triangle shown here at the heart of the figure. It is a 45-45 right triangle, with sides in the proportions, 1, 1, and sqrt(2). Thus the ratio of the radii is sqrt(2). |
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