19. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Special Point of Intersection

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This Demonstration constructs a triangle given the length of its base , the difference of the base angles and the point , the intersection of and , where is the circumcenter.

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Construction

Step 1: Draw a segment of length and a point on between and . Let be the midpoint of .

Step 2: Let be the intersection of the perpendicular bisector of and the ray through that forms the angle with .

Step 3: Draw a circle with center and radius . Let be the intersection of and .

Step 4: Triangle is a solution of the problem.

Verification

The circle is the circumcircle of triangle , 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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