Circles (A58a) and (A58b): Bui chords circles

Definition

In the Arbelos draw the points D and E on semicircle (O), in such a way that DO1 and EO2 are perpendicular to AB. DA and DC intercept a chord off (O1) which is a diameter of the Archimedean circle (A58a). Similarly we find (A58b) 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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