Question

(01.03 mc) layla is using her compass and straightedge to complete construction of a polygon inscribed in a circle. which polygon is she in the process of constructing? a an equilateral triangle b a square c a regular pentagon d a regular hexagon

Explanation:

Step1: Recall polygon construction methods

To construct a square inscribed in a circle, we first draw a diameter of the circle. Then we construct a perpendicular bisector of this diameter (which is another diameter). These two diameters (perpendicular to each other) divide the circle into four equal arcs. Connecting the endpoints of these diameters (the four intersection points of the diameters and the circle) gives us a square.

Step2: Analyze other options

• For an equilateral triangle: We would divide the circle into three equal arcs (using a \(120^{\circ}\) central - angle), not two perpendicular diameters.
• For a regular pentagon: We use more complex angle - measure (central angles of \(72^{\circ}\)) and construction steps based on the golden ratio, not two perpendicular diameters.
• For a regular hexagon: We can use the radius of the circle to mark off arcs (since the side - length of a regular hexagon inscribed in a circle is equal to the radius of the circle), not two perpendicular diameters.

Answer:

b. A square