Answer:
Max possible red points = 220
Step-by-step explanation:
- Remark that a convex quadrilateral has exactly one intersection which is the intersection of its two diagonals.
- Consider 9 points on the circle, which give at most ( combination ):
[tex]\frac{9!}{4!5!} = 126[/tex] intersections.
- Now consider the center and the three points on the circle, there are at most ( combinations ):
[tex]\frac{9!}{3!6!} = 84[/tex] intersections.
- So the total number of red points would be:
Given = 10
2 Diagonals = 126
Center + 3 pts = 84
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Max possible red points = 220
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