Circles (A20a) and (A20b): The lifted cousin circles

Definition

The centers A20a and A20b of these circles are the highest points of (A5a) and (A5b) and they pass through the centers of (A5a) and (A5b) [Dodge et al 1999].

Properties

  1. 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 (A5a) and (A5b). [FvL, 17 Mar 2008]
  2. Let E and F be the midpoints of (O1) and (O2) respectively. Then A20a is the point of intersection of AF and CE, A20b is the point of intersection of BE and CF, while the point of tangency G of (A20a) and (A20b) is the point of intersection of O1F and O2E. [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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