13. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Difference of the Lengths of the Other Two Sides
This Demonstration shows a construction of a triangle given the length of the base , the difference of the lengths of the other two sides and , and the difference of angles at the base.[more]
Step 1: Draw a line of length and a circle with center and central angle over the chord . Measure out the point on the circle at distance from .
Step 2: Let the point be the intersection of and the right bisector of .
Then satisfies the given conditions.
Let and .
By construction, . By step 2, , so , the difference of the other sides.
Since the central angle by construction, . The line bisects the angle at . In any triangle, the , ; since is isosceles, . So and .[less]
 D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009 p. 95.