GeoGebra 4.0: Triangle Circumcenter Construction Activity: Triangle Circumcenter Construction •
Objectives 1. Becoming familiar with the basic use of tools and formatting 2. To understand the properties of a triangle and how they can be used to construct a circumcircle. Introduction: In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin with the actual construction of the circumscribed circle: Polygon Circle with center through point Perpendicular bisector Move Intersect two objects Hint: If you are not sure about the construction process, you might want to have a look at the file, Circumcenter.ggb. Preparing the Window: • Open a new GeoGebra file. • Hide the algebra window, the axes on and the input field. Set labeling to New Points Only. Construction process: 1. Use the polygon tool to create an arbitrary triangle ABC 2. Use the perpendicular bisector tool to construct the perpendicular bisector for each side of the triangle. Hint: The tool, perpendicular bisector, can be applied to an existing segment. 3. Use the Intersect two objects tool to mark the intersection point D of two of the line bisectors Hint: The tool, Intersect two objects, can’t be applied to the intersection of three lines. Either select two of the three line bisectors successively, or click the intersection and the program will select the 2 lines for you. 4. Use the Circle with Center Through Point tool to construct a circle with center D through one of the vertices of triangle ABC 5. Perform the drag test to check if your construction is correct. GeoGebra 4.0: Triangle Circumcenter Construction The following Image is what your file should look like before hiding or formatting any objects. Challenge: Modify your construction to answer the following questions: 1. Can the circumcenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true? 2. Try to find an explanation for using line bisectors in order to create the circumcenter of a triangle.