Back to aiming systems including CTE.
I am a "double the distance" outward from the center of the OB to the contact point on same aimer. This serves me well for cut angles less than 30 degrees (CTE) - where the aim point/s is/are on the OB. I was looking for a better way to aim at those cut angles greater than 30 degrees where the aim line is off of the edge of the OB and on the felt and so I studied CTE aiming with the cue being parallel offset to points on the OB and pivot back to center.
If I start at the CTE line, and then parallel shift the cue to aim at the center of the OB and pivot back to the center of the CB, I found that I could make thin cuts i,e.,<90 degrees.
I surmised that if I look at the contact point that sends the OB to the pocket/target on the OB and the distance from that point to the edge of the OB, I could parallel shift that distance from the center of the OB toward the relevant edge of the OB and pivot back to the center of the OB, I would arrive at the double distance point (GB?) that is off of the relevant edge of the OB.
So I can now aim all cut angles by referencing points on the OB rather than off of it to aim lines on the felt for angles greater than 30 degrees.
The parallel offset get smaller as the OB appears to get smaller and the included angle to the GB gets smaller as well - so that the CB is not sent at the same angle as when the OB is closer to the CB which could send the CB sailing past the OB without contact.
Some posters here understand the relevance of the smaller appearing OB down table whereas some are stuck in the 2D diagrams as viewed from above where the CB and OB are the same diameter. Those that understand foreshortening, vanishing point and perspective benefit from that visualization and are successful in utilizing/incorporating it in their aiming.
Diagrams requested.
Please focus on "A" for they are the same distance.
View attachment 213467
Correction for arrow pointing.
View attachment 213469
Just saying.

:thumbup:
Disregard this diagram for the arrows are not pointing correctly.