Question

what is the next step to complete the construction of the square?
construct a tangent at point g perpendicular to (overline{gh}).
construct another diameter perpendicular to (overline{gh}).
construct any chord perpendicular to (overline{gh}).
construct a radius perpendicular to (overline{gh}).

Explanation:

To construct a square inscribed in a semi - circle (assuming the semi - circle is part of the construction context), we need to create another diameter perpendicular to the existing one. A square inscribed in a circle has its diagonals as the diameters of the circle. Since we have a semi - circle and a line (which can be thought of as part of a diameter), constructing another diameter perpendicular to it will help in finding the vertices of the square. A tangent at a point on the semi - circle won't directly help in constructing the square. A chord is not sufficient as it doesn't guarantee the right angles required for a square. A radius perpendicular to the given line is not the key step; we need a diameter.

Answer:

Construct another diameter perpendicular to $\overline{GH}$.