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