| Consider the equilateral triangle enclosed in two circles, as shown here. We need to recall, from Euclid, that the line segment from the center of the triangle (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 30-60 right triangle, with sides in the proportions, 1, 2, and sqrt(3). Thus the ratio of the radii is 2. |
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