Which point is the intersection of the three medians of a triangle?

• A. Incircle
• B. Circumcircle
• C. Centroid
• D. Orthocenter

Answer: (C)

The key idea is that the medians of a triangle are the lines from each vertex to the midpoint of the opposite side, and all three medians meet at a single point inside the triangle. This common point is called the centroid. The centroid has the special property of dividing each median in a 2:1 ratio, with the longer segment closest to the vertex. It also serves as the center of mass for a uniform triangular lamina. The other named centers come from different defining lines: the incenter is where the angle bisectors meet and is the center of the inscribed circle; the circumcenter is where the perpendicular bisectors meet and is the center of the circle through all three vertices; the orthocenter is where the altitudes meet. Since only the centroid is the intersection of all three medians, that is the point described.