29. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Sum of the Other Sides
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This Demonstration shows how to construct a triangle given the length of side , the opposite angle at and the sum of the lengths of the other two sides .[more]
1. Draw the segment of length .
2. Draw the circle with center so that .
3. Draw the circle with center and radius . The circles and meet at and .
4. Let the point be the intersection of the segment and the perpendicular bisector of .
5. Then is the required triangle.
since it is an arc corresponding to the central angle Since is an isosceles triangle with apex , and .
Contributed by: Izidor Hafner (April 2018)
Open content licensed under CC BY-NC-SA
The problem was posed in [1, section IX, problem 8, solution p. 295].
 M. Bland, Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved, Cambridge: J. Smith, 1819.