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Simson lines and deltoids

Published online by Cambridge University Press:  01 August 2016

J. K. R. Barnett
J. K. R. Barnett*
Affiliation:
27 Highcroft Lane, Horndean, Waterlooville P08 9NX, e-mail:jkrb@verlan.demon.co.uk
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For any triangle, and any point on its circumcircle, the feet of the perpendiculars from the point to the sides of the triangle are collinear. The line through them is the Simson (pedal, Wallace, or Wallace-Simson) line. If two circles have radii in ratio 1:3, and the smaller rolls within the larger, a fixed point on the circumference of the smaller describes a deltoid (or tricuspid hypocycloid) curve (Euler, 1745). The envelope of the Simson lines of any triangle is a deltoid.

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Type
Articles
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The Mathematical Gazette , Volume 85 , Issue 504 , November 2001, pp. 446 - 457
Copyright
Copyright © The Mathematical Association 2001

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