Find the bisector of the angle <ABC in the Poincaré plane, where    A=(0,5), B=(0,3) and C=(2,\sqrt{21})

Let l=2L\sqrt{5} and P=(1,2) in the Poincaré plane. Find the uniqe line l' through P    such that l' is orthogonal to l

Construct a triangle in the Poincare plane with all sides equal to ln(2).   (Hint: Use the fact that, the circle with center (0,a) and radius ln(r), r>1 in    the Poincaré plane is equal to the point set       { (x,y) : x^2+(y-1/2(r+1/r)a)^2=1/4(r-1/r)^2a^2 }