Poincaré Disk - Hyperbolic Lambert
ABCD is a Lambert quadrilateral constructed in the Poincaré Disk model of hyperbolic geometry.
Point C is fixed to be the intersection of the line perpendicular to DA through D and the line perpendicular to AB through B.
Points A, B, or D can be moved and point C will adjust accordingly, as will the angle measures shown on the left.
If either one of A or B is moved, it can be moved freely and the other will remain fixed in place. Point D can only be moved so that it remains on a line perpendicular to AB.
(Due to software limitations, sometimes C will "disappear" and be "replaced" by C_1. In this case read the angles given by C_1 instead of those given by C. If neither C nor C_1 appear, then the intersection of BC and DC is outside the disk, i.e. is no longer a valid point in our hyperbolic model.)