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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

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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 .

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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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Contributed by: Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA

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Reference

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

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