Below is a different arrangement of the similar quadrilateral generalization of an associated result of the Van Aubel configuration given at: An associated result of the Van Aubel configuration and some generalizations.
Van Aubel Similar Quadrilateral Generalization 2
Given four points A, B, C, D, and four directly similar quadrilaterals AP1P2B, CQ1Q2B, CR1R2D, AS1S2D with respective centroids P, Q, R, S. Further let F, G, H, I be the midpoints of the segments AC, BD, QS, PR respectively. Then GHFI is a kite.
An associated result of the Van Aubel configuration and its generalization: Different Arrangements
Similar rhombi special case
To view & manipulate a similar rhombi special case of this result, navigate to it using the appropriate button in the ABOVE dynamic sketch.
Similar parallelogram case
Also use the button above to view a completely different placement of similar parallelograms, where GHFI is a cyclic quadrilateral, and which is a generalization of the Pellegrinetti circle for the standard Van Aubel configuration with squares on the sides.
Published paper
De Villiers, M. (2023). An associated result of the Van Aubel configuration and its generalization. International Journal of Mathematical Education in Science and Technology, Vol 54, no 3, pp. 462-472.
Related Links
An associated result of the Van Aubel configuration and some generalizations
Some further generalizations of an associated result of the Van Aubel configuration using pairs of similar triangles
A Fundamental Theorem of Similarity
Van Aubel Centroid & its Generalization
Van Aubel's Theorem and some Generalizations
Twin Circles for a Van Aubel configuration involving Similar Parallelograms
Quadrilateral Balancing Theorem: Another 'Van Aubel-like' theorem
Generalizations of a theorem of Sylvester (about forces acting on a point in a triangle)
Napoleon's Theorem: Generalizations & Converses
Some Variations of Vecten configurations
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Created with WebSketchpad 18 May 2021 by Michael de Villiers; updated 19 February 2022; 24 November 2022; 13 August 2025.