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On the Connection between the Inscribed and Escribed Circles of a Triangle

Published online by Cambridge University Press:  03 November 2016

H. B. Billups
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Extract

The chief object of this paper is to investigate a method of obtaining from any proposition connected with the inscribed circle of a plane triangle a corresponding proposition connected with one of the escribed circles of a plane triangle.

If we let a, b, c represent three lengths and A, B, C three angles, with the following limitations:

I. All six quantities must be positive,

II. A + B + C = π,

III.

we can regard a, b, c, A, B, C as the sides and angles of a plane triangle, and then by the methods of Algebra and Trigonometry we can deduce a number of algebraical and trigonometrical relations connecting them.

Type
Research Article
Information
The Mathematical Gazette , Volume 1 , Issue 14 , June 1898 , pp. 177 - 180
Copyright
Copyright © Mathematical Association 1898

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