IO540,
I find that I generally agree with your comments on the various threads, but not on this one.
Whilst I initially answered to what I thought was a totally academic question, I am sure that the use of the 'speed to beacon' would be easily the best method to get there.
Whilst for the academic addressing of the question I suggested 10deg and 2 knots difference, in reality, use 30deg and 50kts!
As long as the speed to the beacon is kept positive, ie with distance reducing, you will eventually get there, even if its as low as 10kts, and you go spiralling round it. The only time you will not get there is if you let the speed to beacon drop to zero, ie you are passing abeam.
In practice, keep the DME speed display high, say within 50kts of max, keep on top of whether turning left or right increases/reduces the displayed speed, don't worry about 20kt variations, and you will see the ground distance to beacon (allowing for slant range) drop to less than a mile.
This is the mathematics of large angles!
Please try it, I have, hence the delay in my response.
MikeJ
p.s. I do have a degree in maths.