In the diagram attached, I have to show that:
curly r-bar = sqrt(h^2 + curly-r squared - sqrt(2).h.curly-r).
So far, I've only been able to come up with the obvious fact that:
curly - r^2 = sqrt(h^2+h^2) = sqrt(2).h
A geometry proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.