Question

mel is teaching travis how to use a compass and a straightedge to construct a square inscribed in a circle. he tells travis to begin by using a straightedge to draw any chord of the circle and label it (overline{wx}). next, his instructions are to use the tools to construct a chord that is a perpendicular bisector of (overline{wx}), and label it (overline{yz}). finally, he directs travis to use a straightedge to draw the four chords that make up the square: (overline{wy}), (overline{yx}), (overline{xz}), and (overline{zw}). what is the first error, if any, mel made in his instructions to travis?

a. mels instructions contain no errors.

b. chord (overline{wx}) must be a diameter of the circle.

c. chord (overline{yz}) is found by constructing a segment congruent to (overline{wx}).

d. the four chords that make up the square are the perpendicular bisectors of (overline{wx}) and (overline{yz}).

e. chord (overline{wx}) must be congruent to the radius of the circle.

Explanation:

To construct an inscribed square, the first chord needs to be a diameter (a chord passing through the circle's center). A perpendicular bisector of a non-diameter chord will not be a diameter, so the resulting segments cannot form a square. Mel's error is not specifying that $\overline{WX}$ must be a diameter.

Answer:

B. Chord WX must be a diameter of the circle.