Question

what part of the construction ensures that the vertices of the square inscribed in a circle are evenly spaced along the circle?
drawing two perpendicular diameters of the circle
constructing perpendicular bisectors of the circles diameter
marking four points at equal distances along the circumference
dividing the circle into four equal arcs

Explanation:

When we inscribe a square in a circle, drawing two perpendicular diameters (which is equivalent to constructing perpendicular bisectors of the circle's diameter) divides the circle into four equal - arcs. The endpoints of these diameters (the points where they intersect the circle) are the vertices of the square. These four points are evenly spaced along the circle. Marking four points at equal distances along the circumference is not the standard construction method for an inscribed square. Dividing the circle into four equal arcs is a result of drawing two perpendicular diameters. So, drawing two perpendicular diameters of the circle ensures the vertices of the inscribed square are evenly spaced.

Answer:

A. Drawing two perpendicular diameters of the circle