Constructing a Triangle via the Centroid Line (Schwerliniendreieck)

This GeoGebra example demonstrates a triangle configuration built from the centroid (Schwerpunkt) idea—using the centroid line / side bisector concept to generate key lines, intersection points, and circle-based relationships. The core concepts are triangle midlines and the centroid, constructions using midpoints of the triangle’s sides, and geometric solving of intersections between lines and circles. The construction uses Polygon to create triangle ABC; Point and Midpoint to mark vertices and compute side midpoints; Segment and Line to draw the triangle edges and the relevant centroid/median (Schwerlinie/Seitenhalbierende-type) lines; Circle to define the circle (including an inner-circle–related circle); and Intersect to obtain the critical intersection points (such as A′, C′ and related points) that complete the configuration. Suitable for high-school geometry learning, classroom visualization of centroid properties, and early preparation for optimization/extremum tasks that benefit from strong geometric intuition.