Let O designate the centre of an equilateral triangle. Points U-Z are chosen at random within the triangle. We have learnt that points U,V,W are each nearer to a (possibly different) vertex than to O; while X,Y are each closer to O than to any of the vertices.

Show that triangle XYZ is more likely than triangle UVW to contain the point O within its interior.

Steve,

You did really well, even if you tired out a little bit near the end.

Would it encourage you to learn that my solution used very many of these same ideas? They just need to be carried forward a little further. (To be honest, you still miss one key insight).

I hope you will try again. Just do a Cauchy inversion on your neuron activation list (or something) and you'll be surprised to find yourself in the surrounded by the solution!