@tomleslie I thank you first for the helpful observation and then for your detailed answer. 

It will take me some time to digest this and I may have follow-on questions.

I am new to hyperbolic geometry and only recently learned how to create a hyperbolic circle and a hyperbolic line through any two points in the Poincare disk. This is a fascinating branch of geometry!  

@tomleslie I can't remember why I drew my Poincare disk centred at [1,1].

Would shifting the disk and the points within it so the disk was centred at [0,0] help you or another respondent to provide an answer?

If yes, I will do so and resubmit my question. 

@mmcdara The extra "verbosity" in your reply gives me additional understanding.

@dharr Your reply helps  me progress in Stillwell's book.

@dharr Sorry for the delay in replying, somehow your email to me went to spam. 

@acer My table is a table data structure. Save and read work perfectly and seem to be the simplest way to share the table between worksheets.

@Joe Riel I fixed the unmarked comment and also applied Acer's fix to geom3d[point] and my worksheet executes properly.

@acer After applying your fixes my worksheet executes properly.

I'm glad you are available to help.

@mmcdara I'm out of town for a few days and then I will chase down the references you have mentioned and let you know what I find. 

Here is a worksheet showing an inellipsoid lying obliquely in a tetrahedron. It requires a link to the DirectSearch package.

Inellipsoid_in_a_tetrahedron.mw

I also have worksheets showing inellipsoids lying vertically and horizontally in a tetrahedron.

@vv Maple's own solve command produces a correct inellipse within about one second.

@vv Thank you, vv. Does this mean that an inellipse exists for any two points of tangency, each on a different side, in any shape of triangle?

@Pepini You might be interested in this.

Contour_colored_bands.mw

@Kitonum Thank you for advancing my understanding.

@acer Thanks for this info, I didn't realize the effect abs would have on the plotted expression.

Does Maple Learn have a 3D capability?