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A generalisation of the arbelos theorem of Archimedes

Published online by Cambridge University Press:  23 January 2015

Shailesh A Shirali
Shailesh A Shirali*
Affiliation:
Rishi Valley School, Rishi Valley 517 352, Andhra Pradesh, Indiae-mail:shailesh.shirali@gmail.com
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Extract

Over two thousand years ago, Archimedes discovered a remarkable result concerning two circles drawn with reference to a configuration of three circles and a straight line. Figure 1 displays this result.

In the figure, A, B, C are three collinear points, with B between A and C; circles ω1, ω2, ω3 are drawn on AB, BC, AC as diameters, respectively; a line l is drawn through B, perpendicular to AC; a circle ω4 is inscribed in the region bounded by {ωl, ω3, l}; and a circle ω5 is inscribed in the region bounded by {ω2, ω3, l}. The Archimedean property is that ω4 and ω5 have equal radii.

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 533 , July 2011 , pp. 197 - 205
Copyright
Copyright © The Mathematical Association 2012

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References

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