Euler Line Exploration: Interactive Triangle with Circumcenter, Centroid & Ortho

This interactive GeoGebra applet demonstrates the Euler line property in triangles - showing that the circumcenter, centroid, and orthocenter are always collinear regardless of triangle shape. Users can dynamically drag vertices A, B, and C to modify the triangle and observe how these three special points relate to each other along the Euler line. The construction uses perpendicular bisectors (LineBisector) to locate the circumcenter, perpendicular lines (OrthogonalLine) through each vertex to find the orthocenter, and midpoints (Midpoint) combined with intersection points (Intersect) to determine the centroid. This visualization is ideal for middle and high school geometry lessons, suitable for students learning about triangle centers, the Euler line theorem, and exploring how the relative positions of these points change in acute, right, and obtuse triangles.