Seems unnecessarily complicated to me. And there is that word "exact" appearing more than once in the diagram, which is a bit worrying. A compass with a felt tip pen and a small wooden block that hugs the mirror is all you need; like I posted on the
Centre Spotting Discussions thread.
The point of using a compass is that nothing needs to be exact. You keep the compass opening at just approximately half the mirror diameter, and then draw three arcs at approx 120 degrees apart, and this will show very accurately where the centre is. And for extra precision, you simply repeat the steps with the compass opening readjusted so the pen tip strikes closer to centre. Then you can place the sticky-backed spot carefully with tweezers. (The drawings may be a bit misleading, with the spot fitting so neatly inside the triangle. No need to be precise. But you do need a reasonably good compass without any backlash.)