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Many familes of lines form an envelope, that is, a curve each of whose points is a point of tangency with one of the lines. Here, you see such a family of lines, each being the Euler line of a triangle DEF that is similar to and inscribed in the given triangle ABC.

The set of all triangles DEF "twirls" as point D moves on side BC, and the Euler line of DEF twirls through the envelope of tangent lines.

For more, see GEOMETRY IN ACTION, Chapter 8, Project 5.