line segment as one side; place the point of the compass on one end of the line, then swing an arc from that point to the other point of the line segment; repeat with the other side of the line, which connects the point where the two arcs intersect with each end of the line segment in the aftermath.

If three equilateral triangles are constructed on the sides of an arbitrary triangle, either all outward or inward, by Napoleon's theorem the centers of those