Quiz

I wrote that the problem can be reduced to a 2D plane and it can be proven that for any point inside a convex polygon, it is possible to draw a perpendicular to one of the sides, such that the end of the perpendicular falls on the side itself, and not its extension. Well, there you basically divide this thing into triangles with angles vertex-vertex-center and calculate the heights, maybe it's also worth considering the 360 degrees and so on, I don't feel like solving it further.