Let E and F be the midpoints of (O1) and (O2) respectively.
Then let A61a be the point of intersection of BE and (O1), and A61b the point of intersection of AF and (O2).
Let G of be the point of intersection of O1F and O2E. The circles centered at A61a and A61b passing through G are Archimedean.
[Dao Thanh Oai, june 2014]
Source: A. Bogomolny, Dao's Archimedean Twins from Interactive Mathematics Miscellany and Puzzles http://www.cut-the-knot.org/m/Geometry/DaosTwins.shtml
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