"Scenario B" was found to be correct.

The inner sector of the BBC is a lattice of hexagons like this. [NOTE: for some reason my picture of the BBC inner tiles from the BBC page isn't displaying. It is attached below.]

On the BBC page (http://www.star.bnl.gov/public/bbc/geom/front_view.html) we're told "The small regular hexagons can be inscribed in a circle of diameter 9.64 cm". I think this can be drawn only one way, but to humor all possibilities we can have two scenarios
scenario A = hexagon inscribed inside circle
scenario B = circle inscribed in hexagon

Scenario A corresponds to my understanding of the above quote from the BBC page. These scenarios are drawn below [NOTE: if you can't see it please look at the attached TileDimensions.png]

In either case take the circle to be the same size: diameter = 9.64cm. The "height" of the hexagon is important for knowing the eta coverage of the detector. Event planes and triggers don't need to know the coverage exactly, but it is necessary to know for BBC-EPD correlation checks. In this case the "height" of the hexagon in scenario A is 9.64cm*sqrt(3)/2 = 8.35cm.

 The inner part of the coverage is half the tile height and the outer part is 2.5 x the tile height.

For scenario A:
~> root
root [0] TVector3 A_Inner(0,0.5*8.348484892,375)
root [1] A_Inner.Eta()
(const Double_t)5.19117128984647014e+00
root [2] TVector3 A_Outer(0,2.5*8.348484892,375)
root [3] A_Outer.Eta()
(const Double_t)3.58247591762155304e+00
Thus coverage for scenario A is 3.58 < |eta| < 5.19

For scenario B:
~> root
root [0] TVector3 B_Inner(0,0.5*9.64,375)
root [1] B_Inner.Eta()
(const Double_t)5.04734057795381208e+00
root [2] TVector3 B_Outer(0,2.5*9.64,375)
root [3] B_Outer.Eta()
(const Double_t)3.43889232156178171e+00
Thus coverage for scenario B is 3.44 < |eta| < 5.05

We know that the EPD comes closer to the beam pipe than the BBC (just look at it now, also see page 15 of  https://drupal.star.bnl.gov/STAR/meetings/star-collaboration-meeting/plenary-session-i/epd) and the EPD is supposed to have eta coverage up to 5.1 which is smaller than the 5.19 from scenario A. Thus there is a discrepancy between scenario A and our understanding of the eta coverage for at least one of the detectors.

We have a BBC tile at OSU which we can measure to confirm. From measurements of a BBC tile using calipers (where green rectangles represent exaggerated channels of glue) [NOTE: if you can't see it please look at the attached TileDimensionsMeasured.png]

The scintillator that the piece was glued to had broken off cleanly so this is enough glue for both tiles.

L1 = 3.7155in = 9.43737cm
L2 = 3.798in = 9.64692cm

L2 - L1 = 0.0825in = 0.20955cm

Therefore scenario B must be correct. Really the largest circle that can be inscribed in the hexagon has a diameter of 9.64cm. I think it would be worth changing the wording on the BBC page.

To give a sense of the measurement I also took a few photos with a ruler showing the L1 measurement. This is RulerMeasurementL1.pdf.

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Additionally there are CAD dimensions from Les, which seem to agree with the promoted conclusion.

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This problem also currently exists in the BBC simulation geometry, the writer of which must have interpreted the page as I did. From
https://drupal.star.bnl.gov/STAR/comp/simu/geometry0/agml-example-beam-beam-counters