I've found that when you need to construct a perpendicular to a given straight line from a given point not on the line, you can build an equilateral triangle with one side on the given straight line and one of the ends of that side in an arbitrary (actually, given) point on the line, and then make a line through the third (not on the given line) corner of this triangle and the given point not on the given line.
This may not always work - if the third corner of the triangle happen to be the same point as the given point. This suggests to me you may be don't properly consider all possible relations within objects being constructed.
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[ 4.4 ms ] story [ 29.7 ms ] threadI've found that when you need to construct a perpendicular to a given straight line from a given point not on the line, you can build an equilateral triangle with one side on the given straight line and one of the ends of that side in an arbitrary (actually, given) point on the line, and then make a line through the third (not on the given line) corner of this triangle and the given point not on the given line.
This may not always work - if the third corner of the triangle happen to be the same point as the given point. This suggests to me you may be don't properly consider all possible relations within objects being constructed.