Poincare Geodesics

More recently I was looking at Odonodo's art. He had a family of circles tangent to radial lines passing through a circle's center. It occurred to me I could do a similar construction, a family of circles tangent to the horizontal line passing through a circle's center. First I constructed a line perpendicular to the circle. Then I cloned and rotated this tangent line about the center. Intersections of these tangent lines give my my circle centers. Here's Odonodo's study:

Circles perpendicular to a disk's perimeter describe geodesics in a Poincare disk (I believe). I'm embarrassed to admit I've never constructed Poincare disk design -- I didn't know how. But by studying Odonodo's and MathIsBeautiful's work I think I now have a handle on it. My thanks to these two artists.