13. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Difference of the Lengths of the Other Two Sides

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This Demonstration shows a construction of a triangle given the length of the base , the difference of the lengths of the other two sides and , and the difference of angles at the base.

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Construction

Step 1: Draw a line of length and a circle with center and central angle over the chord . Measure out the point on the circle at distance from .

Step 2: Let the point be the intersection of and the right bisector of .

Then satisfies the given conditions.

Verification

Let and .

By construction, . By step 2, , so , the difference of the other sides.

Since the central angle by construction, . The line bisects the angle at . In any triangle, the , ; since is isosceles, . So and .

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Contributed by: Izidor Hafner (August 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 p. 95.



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