point of concurrency
A point of concurrency is a specific location where three or more lines, segments, or rays intersect or meet. In geometry, this concept is often discussed in relation to triangles, where the three main points of concurrency are the centroid, circumcenter, and incenter. Each of these points has unique properties and significance in triangle geometry.
For example, the centroid is the point where the three medians of a triangle intersect, and it represents the triangle's center of mass. The circumcenter is the point where the perpendicular bisectors of the sides meet, and it is equidistant from all three vertices. Understanding points of concurrency helps in solving various geometric problems and proofs.