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18. Construct a Triangle Given the Length of Its Base, the Difference of Angles at Its Base and the Point of Intersection of an Angle Bisector with Its Base

This Demonstration shows a construction of a triangle given the length of its base , the difference of the base angles and the point of intersection of the angle bisector with the base .
Construction
Step 1: Draw a segment of length and a point on that segment.
Step 2: Construct the ray from that forms the angle with and the ray from that forms the angle with . Let be the intersection of and .
Step 3: Draw a ray from at an angle from . The point is the intersection of with an extension of the segment .
Step 4: Triangle is a solution of the problem.
Verification
The exterior angle of the triangle at is . So , .

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Reference
[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009.
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