Question 38
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Three points are marked on each side of a triangle, as shown (the corners are not among the marked points).
How many triangles have all three vertices among the nine marked points?
- A 84
- B 27
- C 81 Correct
- D 78
Correct Answer: Option C
All triples: 9C3 = 84
Three points on the same side make no triangle: 3 sides × 3C3 = 3
84 − 3 = 81
Trap: 84 forgets the collinear triples.
Answer: 81
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