(1) The locus of the middle H of DE is a line parallel to the side CA. Analogous statements hold for the other sides of the triangle DEF.

(2) More generally, given a number y, the locus of a point H on DE, such that DH/DE = y is a line.

(3) ABC and all the triangles DEF(x) share the same centroid I.

In the figure above varying y shows the position of the corresponding (blue) line, which is the geometric locus referred in (2) of the above proposition. This is discussed also in the file Analogon2.html .

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