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Countless Simson line configurations

Published online by Cambridge University Press:  01 August 2016

C. J. Bradley  and
J. T. Bradley
C. J. Bradley
Affiliation:
Clifton College, Bristol BS8 3JH
J. T. Bradley
Affiliation:
Department of Computer Science, University of Bristol BS8 1TR
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Extract

The Simson line property is normally associated with points on the circumcircle of a triangle. It is embodied by the following theorem.

Given any triangle ABC and a point P in the plane of the triangle, if perpendiculars from P on to the sides BC, CA, AB meet those sides at L, M, N respectively then L, M, N are collinear if and only if P lies on the circumcircle of triangle ABC. The line LMN is then known as the Simson line of P.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 80 , Issue 488 , July 1996 , pp. 314 - 321
Copyright
Copyright © The Mathematical Association 1996

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