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Steiner-Lehmus and the Feuerbach triangles

Published online by Cambridge University Press:  01 August 2016

C. F. Parry*
Affiliation:
73 Scott Drive, Exmouth EX8 3LF

Extract

In the geometry of the triangle, the Feuerbach quadrangle comprises the four points of contact between the nine point circle and the four tritangent circles. By omitting each of the four points in turn, we create four Feuerbach triangles. When the basic triangle is isosceles we find that two of the four points of contact coincide and the resultant single Feuerbach triangle is also isosceles. In the spirit of Steiner-Lehmus we address the converse question – if one of the Feuerbach triangles is isosceles, is the basic triangle necessarily isosceles? The answer is negative.

Type
Articles
Copyright
Copyright © The Mathematical Association 1995

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References

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