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Two triplets of circum-hyperbolas

Published online by Cambridge University Press:  20 January 2009

R. Tucker
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1. Let one of the series of circles, which can be drawn so as to touch the sides AB, AC of a triangle, touch those sides in K, L; and let AK = AL = δ.

Then the points K, L are

and the lines BL, CK are givn by

Hence eliminating δ we get for the locus of P the hyperbola

The allied hyperbolas are

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , February 1893 , pp. 69 - 75
Copyright
Copyright © Edinburgh Mathematical Society 1893

References

* The mode of procedure adopted in the following paragraphs is the same, viz., p, q, r points are on BC, CA, AB respectively.

† The polars of (–1, 1, 1), (1, – 1, 1), (1, 1, – 1) are respectively

(∴ this is the isogonal conjugate of the polar of the incentre),