Question

josefina is inscribing a square in a circle with center c. she first uses a straight edge to draw a diameter of the circle through the center. what is her next step?
a. using a compass and straight edge, construct two perpendicular lines that intersect the endpoints of the diameter.
b. using a compass and straight edge, construct two lines parallel to the diameter tangent to a point on the circle.
c. using a compass and straight edge, construct the perpendicular bisector of the diameter.
d. using a straight edge, draw an acute angle from one endpoint of the diameter to the circumference of the circle.

Explanation:

Step1: Recall the property of inscribed square

An inscribed square in a circle has its diagonals as the circle's diameters and the diagonals are perpendicular bisectors of each other.

Step2: Analyze each option

• Option A: Constructing two perpendicular lines through the endpoints of the diameter won't form an inscribed square.
• Option B: Constructing parallel lines tangent to the circle won't help in forming an inscribed square.
• Option C: Constructing the perpendicular bisector of the diameter (which is also a diameter) will give two perpendicular diameters. Connecting the four intersection points of these diameters with the circle forms a square.
• Option D: Drawing an acute - angle won't help in constructing the square.

Answer:

C. Using a compass and straight edge, construct the perpendicular bisector of the diameter.