More Shapes of Central Quadrilaterals

Stanley Rabinowitz; Ercole Suppa

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arXiv · 2509.12219

More Shapes of Central Quadrilaterals

Stanley Rabinowitz·Ercole Suppa

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Abstract

Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, and for various choices for E, we examine the shape of the central quadrilateral. Using a computer, we determine when the central quadrilateral has a special shape, such as being a rhombus or a cyclic quadrilateral. A typical result is the following. Let E be the centroid of equidiagonal quadrilateral ABCD. Let F, G, H, and I be the X(591)-points of triangles ABE, BCE, CDE, and DAE, respectively. Then FGHI is an orthodiagonal quadrilateral

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Stanley Rabinowitz, Ercole Suppa. 2025-09-02. More Shapes of Central Quadrilaterals. https://arxiv.org/abs/2509.12219

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