[Note: if you are not familiar with the nine-point circle already, you may wish to see the next post on this blog, where it is explained in detail.]

The largest circle shown here is the circumscribed circle for a large equilateral triangle, and its nine-point circle is shown as well. Also, each altitude of an equilateral triangle splits it into two 30-60-90 triangles. Since there are three such altitudes, there are six 30-60-90 triangles of this size — and all their nine-point circles are shown as well. These three altitudes, taken together, also split the equilateral triangle into six smaller 30-60-90 triangles, and their nine-point circles are also shown here.

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