The circle through C tangent to the tangent from A to the circle with center B through C is Archimedean. Similarly the circle through C tangent to the tangent from B to the circle with center A through C is Archimedean. [FvL, 27 sep 2007].
Consider the tangents from O1 to (O2) and O2 to (O1) intersecting at H.
Create J in such a way that triangle JO1O2 has H as its incenter.
JO1 meets (O1) in K and the circle with diameter CK is Archimedean circle (A50a).
JO2 meets (O1) in L and the circle with diameter CL is Archimedean circle (A50b).
[Miguel Ochoa Sanchez (conjecture) and Emmanuel Antonio José García (proof), june 2014]
Source: A. Bogomolny, Shedding Light on the Ball for Eyeballing from Interactive Mathematics Miscellany and Puzzles http://www.cut-the-knot.org/pythagoras/LightingTheBall.shtml
Back to Catalogue