Question

select the correct answer.
in her notebook, pia wrote these steps to construct a square inscribed in a circle:
use a compass and a straightedge to find chord lm, which is the perpendicular bisector of jk. then, use a straightedge to draw the four chords that make up the square: jl, lk, km, and mj.
which instruction is pia missing?
a. draw any chord on a circle and label it jk.
b. draw any diameter on a circle and label it jk.
c. construct a secant passing through points j and k on a circle.
d. construct a tangent passing through point k on circle j.
e. construct radius jk on circle j.

Explanation:

To construct a square inscribed in a circle, we need to follow certain geometric construction steps. The first step in constructing a square inscribed in a circle is to draw a diameter. A diameter is a chord that passes through the center of the circle. If we start by drawing a chord (Option A), it may not pass through the center. A secant (Option C) is a line that intersects the circle at two points. A tangent (Option D) touches the circle at only one point. Constructing a radius (Option E) is not the first step for constructing a square inscribed in a circle. The key property for constructing a square inscribed in a circle is that the diagonals of the square are diameters of the circle. So, the first step should be to draw a diameter.

Answer:

B. Draw any diameter on a circle and label it \( \overline{JK} \)