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Hagge circles and isogonal conjugation

Published online by Cambridge University Press:  01 August 2016

Christopher Bradley  and
Geoff Smith
Christopher Bradley
Affiliation:
6A Northcote Road, Clifton, Bristol BS8 3HB
Geoff Smith
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, e-mail: G.C.Smith@bath.ac.uk
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Extract

Let Q be a point on the circumcircle of triangle ABC. The reflections of Q in the three triangle sides are known to be collinear, and the line thus defined contains the orthocentre H. This fact can form the basis of a proof of the existence of the Simson line, or alternatively can be deduced from the existence of the Simson line by enlarging the Simson line by a factor of 2 from the centre Q.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 521 , July 2007 , pp. 202 - 207
Copyright
Copyright © The Mathematical Association 2007

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References

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