Jack, what length is it between upper bound and lower bound?
Okay, I answer: 👉 9.51 cm.
You mean you just spout pure BS.
The difference between upper bound and lower bound is quite easy for everyone to calculate.
8.7321885817025 - 8.723877473067 = 0.00831110863 = 8.3 mm in this case.
Your answer is entirely wrong.
Again, the arc is NOT going along the short path, then jumping out to the difference, then jumping back in.
The difference between both 8.7s METERS arc and chord equals 0.27 cm AKA 2.7 MILIMETERS. 
That's pretty identical!
Again, that is the point.
As you use a smaller and smaller angle the upper and lower bound get closer and closer together, and converge to the true value.
The space between both bound are too big for the difference to afford.
No, it isn't.
That is like saying the diagonal line in a square must be 2 units long, because it is 1 unit for the base, and 1 unit for the height, and that a length of sqrt(2) is too short.
That would be pure BS.
If you want to get even a reasonable approximation from that, what you do instead is use Pythagoras to add them up.
e.g. the short chord is 8.723877473067. So you get half of that, square it, and then add the square of the difference in radii, and then find the square root and double it.
i.e. 2*sqrt((8.723877473067/2)^2 + 0.0951^2) = 8.72595061899.
Nothing like the BS you are getting.
Why did you not mention the space length? 
Because it is not needed. You bringing it up is a pathetic, dishonest deflection.
I have an upper limit and a lower limit.
I don't need to use that useless space.
Why do you keep appealing to it while ignoring the upper limit formed from the tangent?
Why don't you try explaining how the arc can be longer than the tangent?