Question

mary is inscribing a square in the circle shown, but she is having difficulty remembering the process.
which summary describes the basic process for constructing a square inscribed in the circle?
a. create the perpendicular bisector of \\(\overline{fo}\\). then use the points of intersection of the perpendicular bisector with the circle, along with points f and g, to draw the square.

b. set the compass width to the length of \\(\overline{fo}\\), place the point of the compass on the circle, and draw an arc. place the compass on the intersection of the arc and the circle, and repeat the process until the circle is intersected by four arcs. connect the intersection points to form the square.

c. create the perpendicular bisector of \\(\overline{fg}\\). then use the points of intersection of the perpendicular bisector with the circle, along with points f and g, to draw the square.

d. set the compass width to the length of \\(\overline{fg}\\), place the point of the compass on the circle, and draw an arc. place the compass on the intersection of the arc and the circle, and repeat the process until the circle is intersected by four arcs. connect the intersection points to form the square.

Explanation:

$\overline{FG}$ is a diameter of the circle. The perpendicular bisector of a diameter will pass through the center and intersect the circle at two more points. These four points (F, G, and the two new intersection points) are equidistant from the center, and the angles between consecutive points are 90°, forming the vertices of an inscribed square. Options A uses a radius's bisector, which does not yield the correct points. Options B and D use compass widths of radius or diameter, which do not create the 90° angles needed for a square.

Answer:

C. Create the perpendicular bisector of $\overline{FG}$. Then use the points of intersection of the perpendicular bisector with the circle, along with points F and G, to draw the square.