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.

W is the mid-point of the line (XY say) and therefore the centre of a parallelogram VXPY.

First construct the point P on VW produced (VP = 2*VW), then the rest of the parallelogram, giving the positions of X and Y.

Posted by Harry on 2010-05-15 15:31:38