Question

Casey constructed this figure by using a compass and a straightedge to draw circle o and diameter pq. she then used a compass to draw two arcs. she labeled the points where those arcs intersect the circle m and n, and she drew the chords that form the triangle. a circle has a triangle with points p m and n inscribed on it. a horizontal line extends from p on the left toward a point q on the right boundary through a center point labeled o of the circle. if δmnp is equilateral, how did casey draw the arcs that defined points m and n?

a. she used a compass centered at p with a radius set equal to pq.
b. she used a compass centered at o with a radius set equal to po.
c. she used a compass centered at q with a radius set equal to po.
d. she used a compass centered at p with a radius set equal to (pq).
e. she used a compass centered at q with a radius set equal to pq.

Answer 1

Casey used a compass centered at point P with a radius equal to PQ to draw the arcs that defined points M and N. Therefore, the correct option is: d. She used a compass centered at P with a radius set equal to PQ.

Step-by-step explanation:

To inscribe an equilateral triangle within a circle using a compass and a straightedge, Casey would use a compass centered at P with a radius set equal to PQ (the diameter of the circle). Therefore, the correct option is: d. She used a compass centered at P with a radius set equal to PQ. This method ensures that the arcs drawn from P intersect the circle at points M and N such that the resulting triangle triangle MNP is equilateral.