# Circles (A_{20a}) and (A_{20b}): The lifted cousin circles

### Definition

The centers A_{20a} and A_{20b} of these circles are the
highest points of (A_{5a}) and (A_{5b}) and they pass through
the centers of (A_{5a}) and (A_{5b}) [Dodge et al 1999].

### Properties

- Let A' and B' be the points on ray CD such that AC=AÇ and BC=B'C. The incircles
of the squares inscribed in triangles ABB' and ACC' with a vertex coinciding with C
are (A
_{5a}) and (A_{5b}). [FvL, 17 Mar 2008]

- Let E and F be the midpoints of (O
_{1}) and (O_{2}) respectively.
Then A_{20a} is the point of intersection of AF and CE, A_{20b} is the point of intersection of BE and CF,
while the point of tangency G of (A_{20a}) and (A_{20b}) is the point of intersection of
O_{1}F and O_{2}E. [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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