12. Construct a Triangle Given the Length of Its Base, the Perimeter and the Difference of the Base Angles

This Demonstration shows a construction of a triangle given the length of its base , the sum of the lengths of the other two sides and , and the difference of the base angles.

Construction

Let , and .

Draw a line segment of length .

Step 1: Draw a circle with center with central angle above the chord .

Step 2: Measure out the point on the circle at distance from the point on the other side of from . Let the point be the intersection of and the right bisector of .

Verification

Since the central angle equals by construction, . On the other hand, , so .