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20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex

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This Demonstration constructs a triangle given the length of its base, the difference of the base angles and a line that contains .

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Introduce the Cartesian coordinate system with the base for the axis and the origin at the midpoint of the segment . The slope-intercept form of the line is determined by the angle it makes with  and its intercept : the equation is .

Suppose that has coordinates and the coordinates of the circumcenter are . Let be the circumradius. The four independent conditions

1. is on

3.

4. lies on the line through that forms an angle with

determine , , and .

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Contributed by: Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA

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Reference

[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009.

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