BSNS102 Study Guide - Final Guide: Concave Polygon, Simple Polygon

• School: University of Otago
• Department: Business Studies
• Course: BSNS102
• Professor: Drew Stelljes

Document Summary

Figure 12. 24 shows the incenter of a triangle. The incenter is computed by: where p = l1 + l2 + l3 is the perimeter of the triangle. Thus, the barycentric coordinates of the incenter are: The radius of the inscribed circle can be computed by dividing the area of the triangle by its perimeter: The inscribed circle solves the problem of finding a circle tangent to three lines. The circumcenter is the point in the triangle that is equidistant from the vertices. It is the cen- ter of the circle that circumscribes the triangle. The circumcenter is constructed as the intersection of the perpendicular bisectors of the sides. Figure 12. 25 shows the circumcenter of a triangle. To compute the circumcenter, we will first define the following intermediate values: With those intermediate values, the barycentric coordinates for the circumcenter are given by: The circumradius and circumcenter solve the problem of finding a circle that passes through three points.