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Humanoid1

You can modify two of the humanoids by dragging the 24 red points. Two right feet are labeled as points A and B, and the intermediate point X determines a ratio |XB|/|AB|. This ratio is used to dilate other points, and the resulting points determine the intermediate humanoid.

Can you make one of the humanoids stand on its head?

For more, see GEOMETRY IN ACTION, Chapter 7, Project 5.