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

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 .
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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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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