For my telescope, r is 5" and f is 54", so the angle a is: arc sin(5/54) = 5.3128°.   With a
1 7/8" Flat, the Main Mirror's tail will be:
(1 7/8 / 2) / tan 5.3128° = 10.0815" long.
A 12" tube leaves a 1" gap between the outside edge of my 10" Main Mirror, and the outside of the telescope tube.  This 1", plus the 5" radius of the mirror, uses up 6" of the Tail's 10.1", leaving 4.1" of the Tail beyond the edge of the telescope tube.
Using a 1.3" Flat will make a Tail of (1.3 / 2) / tan 5.3128° = 7", leaving a 7" - 6" = 1" extension of the Pime Focus beyond the telescope tube. This would increase my Clear Aperture to 8.7" improving the telescope's performance.