AM 2019 P2 Q8: Linear Regression and Circumcircle Exploration

This GeoGebra example demonstrates a comprehensive problem from the Australian Mathematics Competition (AM 2019 P2 Q8), integrating linear regression, polygon circumcircles, and inequality regions in a dynamic geometry environment. The core mathematical concepts include least-squares linear regression (FitLineY), slope and intercept of a line, properties of circumcircles of polygons (especially triangles), and feasible regions defined by inequalities. Construction highlights: using GeoGebra commands Sequence, Join, TableText to generate data tables, FitLineY for regression line, Slope for slope calculation, and RightSide to extract the right-hand side of inequalities; interactive buttons (button1, button2) control the display, while multiple points, lines (l1 to l7), circles (c, d), and functions (f) are constructed to illustrate geometric relationships. This is suitable for senior high school or pre-university students reviewing linear regression, coordinate geometry, and inequalities, and serves as a dynamic visual aid for competition problems.