# 32b. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C

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This Demonstration shows the construction of a triangle given the length of the base , the ratio of the other two sides and a line containing .

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Contributed by: Gerd Baron, Izidor Hafner, Marko Razpet and Nada Razpet (August 2018)

Open content licensed under CC BY-NC-SA

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## Details

An Apollonius circle is the circle defined by the locus of points for which the ratio of the distances from two given points is a fixed number . In this case, the fixed points are and , and .

The radius of the Apollonius circle is

if . This depends only on and .

Reference

[1] E. J. Borowski and J. M. Borwein, *Collins Dictionary of Mathematics*, New York: HarperCollins Publishers, 1989 pp. 21–22.

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