Answer: Midpoints of sides, feet of altitudes, and midpoints of vertex-to-orthocenter segments.
- A Midpoints of the three sides alone, excluding any other special points
- B Feet of the three altitudes alone, excluding the side midpoints
- C Midpoints of sides, feet of altitudes, and midpoints of vertex-to-orthocenter segments
- D The circumcentre and the incentre of the triangle, and nothing else besides those two points
Correct answer: C. Midpoints of sides, feet of altitudes, and midpoints of vertex-to-orthocenter segments
Explanation: Nine-point circle: passes through 9 notable points -- 3 midpoints of sides, 3 feet of altitudes, and 3 midpoints of segments from vertices to orthocenter.
Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.
Concept context
Perimeters, areas, and volumes of 2D and 3D shapes