Given the points A,B,C, defining lines BA and BC, consider two other points on these lines correspondingly: D = (1-s)B+sA, E = (1-t)B+C, with fixed s, t. On the same lines correspondingly consider also the points G = (1-x)D + xA and H = (1-x)E + xC. Vary the real number x and on the resulting variable line GH(x) consider the point I defined through I = (1-t)H+tG with fixed t. Prove that for variable x and all other data fixed, point I moves on a line (red), passing through F = (1-t)C + tA.
In the file Analogon.html we discuss the relation of point J from B and the other data.
Look at the file Trianalogon.html for an application of this property on the sides of a triangle.
![[alogo]](alogo.png){kind=small}
Analogon-2 ![[0_0]](Analogon2_files/Analogon2_0_0_0.png)
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![[1_0]](Analogon2_files/Analogon2_0_1_0.png)
![[1_1]](Analogon2_files/Analogon2_0_1_1.png)