...Another trick you can use is based on the fact when the focuser axis is aligned to the primary center, then the reflection of the primary is necessarily centered under the focuser. Because the primary mirror is centered under the focuser, we can use the reflection centered under the focuser as a reference to center our diagonal, too.
To be clear, it's not a trick. Making all three circles concentric (ideally, with the apparent size of the actual edge of the secondary mirror only slightly larger than the apparent size of the reflection of the primary mirror, which places the pupil near the apex) is the standard procedure for optimal secondary mirror placement. In fact, it's more difficult to assess the actual secondary mirror placement when the focuser axis is not correct.
There are far too many internet collimation sources that use only two circles (the bottom edge of the focuser drawtube or bottom edge of the sight tube and the actual edge of the secondary mirror) for secondary mirror "alignment". Several of these references actually suggest placing a paper between the secondary and primary mirrors to completely remove the "confusing" reflection of the primary mirror. And too many consider this two circle alignment to be the more critical focuser alignment, or go on to suggest "centering the reflection of the primary in the secondary mirror" as the focuser alignment.
1.) Concentricity of the three circles indicates optimal secondary mirror placement (rotation and offset).
2.) Alignment of the sight tube cross hairs or the outgoing thin beam laser relative to the primary mirror center marker (usually corrected by adjusting the secondary mirror tilt) is focuser axial alignment.
3.) Alignment of the return thin beam laser relative to the laser emitter is primary mirror axial alignment. Or, using a Cheshire derivative (including a collimation cap or Barlowed laser), aligning the reflection of the Cheshire ring to the primary mirror center marker or the silhouette of the primary mirror center marker relative to the Barlowed laser target is also primary mirror axial alignment.
Axial alignment correction delivers image performance, including optimal field focus (focuser axis) and optimally centered coma free images (primary mirror axis). Optimal secondary mirror placement delivers centered field illumination--which has little (or no) impact on the image in an eyepiece, and minimal (but easily corrected) impact on the image in a camera.
...if you want to learn about offset, you can read up on classic offset and the new model. The proper offset happens (almost) automatically. 
I would argue that, since we're talking potential errors around ~1mm (or less), each error impacting the various geometries (squared focuser, spider, centered primary, spider, secondary mirror offset (holder/mirror) and possible skew)... pretty much all "proper" secondary mirror placements are possible because, in one way--or many ways, the vast majority of Newtonian collimation enthusiasts all utilize the New Model paradigm (and some sort of offset) to some "workable" solution. 