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Geometrical Notes

Published online by Cambridge University Press:  20 January 2009

J. S. Mackay
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A straight line KK′ meets the circumference of a circle at two real or two imaginary points K, K′, and H is the middle point of the real or imaginary chord KK′. If A, B, C, D be any four points on the circumference, and the pairs of straight lines AB, DC, AC, BD, AD, CB meet KK′ at the pairs of points E,E′, F,F′, G,G′; then if any one pair of points be equidistant from H, the two other pairs will also be equidistant.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , February 1884 , pp. 38 - 42
Copyright
Copyright © Edinburgh Mathematical Society 1884

References

* Professor Chrystal pointed out that a particular case of this, viz., where the triangle is isosceles right-angled is dealt with in the Annals of Mathematics, I., p. 24, and Mr Fraser has since received from Dr Rennet, of Aberdeen, a reference to Thomas Simpson's Algebra, 2nd edition, (1755) p. 369, where a very general problem of this nature is stated and solved.