Special segments and points of concurrency in triangles

Four special segments live inside every triangle, and each family of three meets at one point of concurrency. A perpendicular bisector of a side passes through its midpoint at a right angle; the three perpendicular bisectors of a triangle meet at the circumcenter, equidistant from all three VERTICES (the center of the circumscribed circle through all three vertices). An angle bisector splits a vertex angle in half; the three angle bisectors meet at the incenter, equidistant from all three SIDES (the center of the inscribed circle touching all three sides).

A median connects a vertex to the midpoint of the opposite side; the three medians meet at the centroid, the triangle's balance point. The centroid divides every median in a fixed 2:1 ratio, vertex-to-centroid compared to centroid-to-midpoint. An altitude drops from a vertex perpendicular to the line containing the opposite side; the three altitudes meet at the orthocenter, which -- unlike the incenter and centroid -- can fall OUTSIDE the triangle when the triangle is obtuse (the circumcenter can fall outside an obtuse triangle too).