Circles (A1a) and (A1b): The Archimedean twins
The Adam and Eve of Archimedean circles in the arbelos.
Through C draw the perpendicular to AB, dividing the arbelos in two parts.
The incircles of these parts are congruent. [Archimedes]
- The circular hull of the Archimedean twins has the same area as the arbelos
itself (and the circle with diameter CD). [Bankoff 1954]
- The common tangent of (A1a) with (O1) passes through B, the common
tangent of (A1b) and (O2) passes through A. [Dodge e.a. 2000]
- The common tangent segment ATb is congruent to AD, the common tangent
segment BTa is congruent to BD. [Dodge e.a. 2000]
- Let N1 be the point where O1A1a meets CD then O1N1 = O1B. Let N2 be the
oint where O2A1b meets CD, then O2N2 = O2B.[Wendijk 2001/Hermann
2003, d'Ignazio and
Suppa 2001 - reworded]
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