Given points ABC, consider two points D = (1-s)B+sC, E = (1-t)B+A, with fixed s, t. On the same lines correspondingly consider also the points G = (1-h)D + hC and F = (1-h)E + hA. Prove that the intersection point H of line CA and line FG is independent of the position of B, provided points A, C and numbers s, t, h remain fixed.

In the above calculation x is the ratio DG/DC = EF/EA. Point B is free movable (switch to the selection-tool CTRL+1) and moving it one sees that H remains constant. A related calculation is made in the file Analogon2.html .