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From nested Miquel triangles to Miquel distances

Published online by Cambridge University Press:  01 August 2016

Michael De Villiers*
Mathematics Education, University of Durban-Westville, South Africa, email:


This article presents interesting generalisations of three well-known results related to pedal triangles and distances, and the Simson line.

The triangle whose vertices are the feet of the perpendiculars from a point P inside a triangle ABC to each of its sides AB, BC and AC, is called a pedal triangle.

Copyright © The Mathematical Association 2002

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1. Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, The Mathematical Association of America (1967).Google Scholar
2. Johnson, R. A., Advanced Euclidean geometry (Modern geometry), New York, Dover Publications (1960).Google Scholar
3. de Villiers, M., Some adventures in Euclidean geometry, University of Durban-Westville: Durban, South Africa (1996).Google Scholar
4. de Villiers, M., Rethinking proof with Sketchpad, Key Curriculum Press, USA (1999).Google Scholar
5. Stewart, B. M., Am. Math. Monthly, 47 (Aug.-Sept. 1940), pp. 462466.CrossRefGoogle Scholar
6. Lockwood, E. H., A book of curves, Cambridge University Press, (1961).CrossRefGoogle Scholar