标题： 更多中心四边形的形状 显示英文标题

标题： More Shapes of Central Quadrilaterals

摘要： 设E是凸四边形ABCD所在平面上的一点。 从E到四边形顶点的连线形成四个三角形。 如果我们在这四个三角形中各确定一个三角形中心，这四个三角形中心将形成另一个四边形，称为中心四边形。 对于各种形状的四边形、1000种不同的三角形中心以及E的各种选择，我们研究中心四边形的形状。 利用计算机，我们确定当中心四边形具有特殊形状时的情况，例如菱形或圆内接四边形。 一个典型的结果如下。 设E是等对角线四边形ABCD的重心。 设F、G、H和I分别为三角形ABE、BCE、CDE和DAE的X(591)点。 则FGHI是一个正交对角四边形。 显示英文摘要

摘要： 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