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Constructing Minimal Area (Posted on 2010-05-13) Difficulty: 3 of 5
In Minimal area, we were asked to find the property of a line which minimized the area of the triangle it completed. It turned out the given point was the midpoint of the third side. In this problem, I am asking for a ruler and compass construction of that line, given the original angle and point.

  Submitted by Brian Smith    
Rating: 3.0000 (1 votes)
Solution: (Hide)
Harry found an easy solution by simply constructing a parallelogram around the angle such that one of the diagonals was the desired line.

My solution is below, based off my solution to Minimal area.
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1. Draw the line through V and M.
2. Construct any line parallel to VM, call that line L. Line L line will intersect one of the rays. Call that intersection A.
3. Extend the other ray into a line, going both directions. The extension will intersect line L, call that point B.
4. Find the midpoint of AB and then draw the line containing the midpoint and V.
5. Construct a line passing through M which is parallel to the line drawn in the last step. This final line is the desired line.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Minimal solution?Bractals2010-05-15 23:05:27
SolutionMinimal solution?Harry2010-05-15 15:31:38
re(2): SolutionBractals2010-05-14 18:22:18
re: SolutionJer2010-05-13 15:07:11
SolutionSolutionBractals2010-05-13 12:55:53
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