THE CREATION OF THE GEOMETRICAL DRAWINGS IN TikZ

Abstract

When solving geometric problems, writing manuals and books on geometry for secondary school and University we have to deal with technical drawings. And even if the drawing is represented quite clearly, move its from the "head" to a paper is quite difficult for many people. To this can help a variety of graphic editors, for example, GeoGebra — the free system of a graphics and calculations which is used for study and teaching of mathematics in schools. However, there is another approach. Geometric drawings can be created using the TikZ system [2], which is an extension package of TEX/LATEX. Using TikZ, not walking out of LATEX, and without resorting to third-party graphical editors, easily write code to output both simple and very complex diagrams, charts, graphs and geometrical drawings. The article discusses the specific of writing code of fragments TikZ to output the drawings for solving typical tasks on planimetry associated with remarkable points in a triangle. Namely, when creating some geometric drawings on those or other data often necessary to calculate and display remarkable points of a triangle, which include: "the centroid (center of mass, centre of gravity)" — the point of intersection of medians; "the orthocenter" — the point crossing heights; "the circle circumscribed around triangle" — the point of intersection "middle" perpendiculars (perpendicular to the midpoints of the sides of the triangle); "the incenter" — the center of the inscribed circle, which is the point of intersection of the bisectors. The following shows how are calculated and returned these points with tikz-code. Also discussed codes for the solution of some auxiliary tasks such as conducting: bisector of an angle; a line which passing through the given point and parallel to the line; a circle with a center at a particular point tangent to a given straight line, etc.