Eight Methods?

The problems (8 methods) .... gives 8 methods.

Look at xxx The collection of methods is impressive, though it would be interesting to analyse the individual methods in terms of dependence and parsimony. Some, eg the trig methods, could be reduced to simple geometry, I imagine. It would then be interesting to consider which could be regarded as genuinely 'independent', ie based on a different mathematics. Perhaps you could get someone to investigate this...