> Hi Narasimham, > > the problem is very interesting. I studied the > special case A=[1 0], B=[0 1], C=[-1 0], D=[0 -1], > where point P is element of the box [-2 2]x[-2 2], > and tet=angle(APB), phi=angle(BPC), psi=angle(CPD). > For the Cross Ratio we have > > CR=sin(tet+phi)*sin(phi+psi)/(sin(tet+phi+psi)*sin(phi > )). > > The result is shown in the attachment. > > Best regards, > Avni
May be you like to sketch a few line loci inside the red area for some particular CR values.