Simulation of Nine-point Circle Using Novel Computing Tools and Investigating the Associated Useful Properties

Abstract

The point, line, triangle and circle are the first set of figures in the world of geometry. The geometries of lines, triangles and circles have been studied and analyzed to obtain some specific and useful results for a long period of time. The analysis and determining various facts in the form of theorems and findings have been carried out by innumerable learned scholars and researchers using the basic tools, logical agreement and testing the data about these figures. The combination of triangle and circle in form of circumscribing circle and in-circle has also been studied at depth. The third fabulous circle is popularly known as the nine-point circle or Feuerbach's circle or Euler circle. The nine-point circle brings in light many interesting and useful properties of the basic triangle. But the construction of the nine-point circle is little tedious and cumbersome. This is because of the facts associated with the nine point circle. Therefore; in this paper the authors have developed a dedicated program in the world famous software MATLAB®. It is attempted to create a large number of triangle data and use them for verifying the useful results in addition to the construction of nine point circle.