19. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Special Point of Intersection

This Demonstration constructs a triangle given the length of its base , the difference of the base angles and the point , the intersection of and , where is the circumcenter.

Construction

Step 1: Draw a segment of length and a point on between and . Let be the midpoint of .

Step 2: Let be the intersection of the perpendicular bisector of and the ray through that forms the angle with .

Step 3: Draw a circle with center and radius . Let be the intersection of and .