Finally I have some time to work through daily problems again. Worked this one last week and forgot to write it up.
When I saw this problem I just saw the trigonometry solution and it blinded me to the symmetry. I guess math is good at showing how what we already know can blind us to the better paths.
So why do mathematicians suck? Well that seemed politer for Konrad than saying he sucks – I worked on this problem for a while and just did not see it. He saw the answer before I was finished describing the problem. So I guess I am the one who sucks, – apologies to mathematicians everywhere.
