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: My paper in the Int. Journal of Math Ed in Sci & Technol. discussing these results has been published online. The first 50 copies are free to download at: An associated result of the Van Aubel configuration and its generalization.
More on Pellegrinetti circle: Click on Twin circles of a Van Aubel Generalization to open a dynamic sketch in a new window.
Created with WebSketchpad 18 May 2021 by Michael de Villiers; updated 19 February 2022; 24 November 2022.