Consider a circle (a) and point C on a diameter AB of it. Construct circles (b), (c) with diameters AC and CB respectively. Draw line (f) orthogonal on AB at C. Then the circles (e), (d) which are simultaneously tangent to a, b, f and a, c, f respectively are congruent (equal radii).

A proof can be given by inverting the figure with respect to a circle with arbitrary radius, centered at C. The proof reduces to a property discussed in the file InversionProperty.html .