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

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.
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 .

### DETAILS

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

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