- AThe three vertices of the triangle, the midpoints of the three sides and the feet of the three altitudes
- BThe midpoints of the three sides, the feet of the three altitudes and the midpoints of the three segments joining the orthocentre to the vertices
- CThe midpoints of the three sides, the feet of the three altitudes and the three excentres
- DThe feet of the three altitudes, the points where the three internal bisectors meet the sides and the midpoints of the three sides
Step-by-Step Solution
The nine points come in three groups of three: the midpoints of the sides, the feet of the altitudes, and the midpoints of AH, BH and CH, where H is the orthocentre. The last group is the one most often forgotten. The vertices themselves lie on the CIRCUMcircle, not on this one; the excentres lie far outside it; and the points where the internal bisectors cut the sides have no reason to lie on it at all.
Answer: B) The midpoints of the three sides, the feet of the three altitudes and the midpoints of the three segments joining the orthocentre to the vertices