Posts tagged 'diophantine'

F.26 Harmonic Conjugate Inversion

For a circle Gamma of center M and radius r on diameter AB, internal point C at x = |MC| and its harmonic conjugate D at y = |MD| are inverses satisfying x*y = r^2, while the tangent DT = T forms a parallelogram M D M_T T whose long diagonal z satisfies z^2 = y^2 + 3*r^2 by Stewart’s Theorem.