Originally Posted by

**ticbol** If the resulting figure is to be a square, then the A,B,C,D must be equally spaced.

Get the midpoint of BC. Call it M.

With M as center, draw semicircles with A and B. (A and D must be on the larger semicircle, while B and C must be on the smaller semicircle.)

Draw a line through M that is perpendicular to the original line. This line will bisect the two semicircles.

Draw a line through A that will pass through the the point of intersection of the larger semicircle and the perpendicular line from M.

Do that too from D.

Draw a line through B that will pass through the the point of intersection of the smaller semicircle and the perpendicular line from M.

Do that too from C.

What is the figure formed now by those four lines?