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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

This Demonstration constructs a triangle given the length of its base, the difference of the base angles and a line that contains .
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
2. is on
3.
4. lies on the line through that forms an angle with
determine , , and .

### DETAILS

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

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