Posts tagged 'ogilvy'

F.12 Coaxial Circles

A hyperbolic pencil of coaxial circles with limiting points L_1 = (-r, 0) and L_2 = (+r, 0) coincides with the Apollonian equipotential circles d_1 / d_2 = k around two point charges Q_1, Q_2, sharing the y-axis as their common radical axis.

F.25 Harmonic Conjugates

Collinear points C and D divide segment AB (of midpoint M and half-length r) internally and externally in the same ratio k = |AC|/|BC| = |AD|/|BD| if and only if |MC|*|MD| = r^2, which occurs if and only if the circle on diameter AB and the Apollonian circle on diameter CD intersect orthogonally.