1. **Problem Statement:** Determine the type of center represented by the black dot in triangle ABC where points D, E, and F are midpoints of sides AB, BC, and AC respectively, i.e., $AD=DB$, $BE=EC$, and $AF=FC$. 2. **Key Concept:** The lines AD, BE, and CF are medians of the triangle because they connect each vertex to the midpoint of the opposite side. 3. **Important Rule:** The three medians of a triangle intersect at a single point called the **centroid**. 4. **Explanation:** - Since D, E, and F are midpoints, segments AD, BE, and CF are medians. - The black dot is the intersection of these medians. - By definition, the centroid is the point where all medians intersect. 5. **Conclusion:** The black dot is the **centroid** of triangle ABC. **Final answer:** Centroid