# Circles (A_{58a}) and (A_{58b}): Bui chords circles

### Definition

In the Arbelos draw the points D and E on semicircle (O), in such a way that DO_{1} and EO_{2} are perpendicular to AB.
DA and DC intercept a chord off (O_{1}) which is a diameter of the Archimedean circle (A_{58a}). Similarly
we find (A_{58b}) from E. [Q.T. Bui, 2011]

Source: A. Bogomolny, A Newly Born Pair of Siblings to Archimedes' Twins from Interactive Mathematics Miscellany and Puzzles
http://www.cut-the-knot.org/Curriculum/Geometry/ArbelosBui.shtml

Rediscovered by: Hiroshi Okumura, Archimedean twin circles in the arbelos, The Mathematical Gazette 97 n 540 (November 2013), p 512

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