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# 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 .

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