In Geometry, we are learning about circumcenters, orthocenters, and centroids of triangles. Geogebra is a nice tool to use to explore how the medians, perpendicular bisectors, and altitudes are concurrent respectively, regardless of the shape of the triangle.
Here is a screenshot of the centroid, which is the intersection of the medians of a triangle:
Here is the circumcenter (the intersection of the perpendicular bisectors), with a circumscribed circle:
And here’s the orthocenter, which is the intersection of the triangle’s altitudes:
A very nice property of the centroid is that it is the exact center of gravity of a triangle. Here’s a brief video of one balancing on a paper clip: