Guess the Centroid! – Interactive Estimation of Triangle's Center of Mass

① This example presents a random triangle with its centroid hidden, inviting users to click where they estimate the centroid lies, then reveals the actual centroid for immediate comparison—a quick formative assessment tool. ② Core mathematical concepts include the centroid (barycenter) of a triangle, defined as the intersection of its three medians, which divides the triangle into six equal-area smaller triangles; related ideas include equilateral triangles, circumcircles, conic sections, and definite integrals. ③ Construction details: using GeoGebra commands Random, Midpoint, Rotate, Ray, Circle, Intersect, Segment, Polygon, PointIn, Line, Distance, and If; objects include points A, B, C, E, F, G, H, I, J, K and various lines, circles, and segments (a, b, c, d, e, f, g, k, l, m, n, p, q, r, s, t1–t9). ④ This is ideal for middle or high school geometry classes, quick classroom polls, or individual exploration to strengthen spatial intuition and understanding of centroid properties.