Should you bash?
Geometry
Level
3
All diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?
70
65
49
128
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1 solution
Drawing a good picture should do it.
A quicker way to see this is to notice that the octagon can be divided into 8 triangles with six intersection points excluding the center. Therefore, the number of intersections is 6 ⋅ 8 + 1 = 4 9 .