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15. Construct a Triangle Given the Lengths of Two Sides and the Median to the Third Side

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This Demonstration shows a construction of a triangle given the lengths and of the sides and and the length of the median from to .

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Construction

Let be a line segment of length and midpoint .

Step 1: Draw a circle with center and radius and a circle with center and radius . Let and be the intersections of the two circles.

Step 2: Extend to the point such that .

Verification

The triangle has side of length .

and bisect each other, so is a parallelogram with sides and . The side has length , and the line segment is the median from of length .

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Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA

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Details

With the condition , the problem has a solution if and only if [1, pp. 287–288].

Reference

[1] A. McFarland, J. McFarland and J. T. Smith, eds., Alfred Tarski: Early Work in Poland: Geometry and Teaching, New York: Birkhäuser, 2014.

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