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31. Construct a Triangle ABC Given the Length of AB, an Adjacent Angle and the Difference of the Lengths of the Other Two Sides

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This Demonstration shows how to construct a triangle given the length of the side , the adjacent angle at and the difference of the lengths of the other two sides .

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Construction

1. Draw the segment of length .

2. Draw a point so that .

3. Let be the intersection of the ray and the perpendicular bisector of .

4. Then is the required triangle.

Verification

Since the triangle is an isosceles triangle with apex , .

Thus .

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Contributed by: Izidor Hafner (April 2018)
Open content licensed under CC BY-NC-SA

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Details

The problem was posed in [1, section IX, problem 1, solution p. 291].

Reference

[1] M. Bland, Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved, Cambridge: J. Smith, 1819.

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