Question

Below is a list of the steps used to construct a square inscribed in a ˚le.

Step M - Place the compass point at the endpoint of the diameter and the pencil at the center of the ˚le to construct an arc.
Step N - Draw in two diameters using the points where the small arc intersects the line segments and the center.
Step O - Construct a small arc by placing the compass point where the diameter intersects the line segment and the pencil on the center of the ˚le.
Step P - Construct a line segment between the two points where the arc intersects the
Step Q - Draw line segments betweel the four points where the two constructed diameters intersect the ˚h
Which list shows these steps in the correct order?
a)M, N, O, P, Q
b) M, P, O, N, Q
c) O, P, M, Q, N
d) Ρ. Ο. Μ. Ο. N

Answer 1

To inscribe a square in a circle, the compass and straightedge construction steps should follow a logical order to ensure vertices touch the circle's circumference. The correct sequence provided is M, N, O, P, Q, as indicated in option a). This involves creating perpendicular diameters and bisecting arcs that intersect the circle at all four vertices of the square.

Step-by-step explanation:

The question involves constructing a square inscribed in a circle, which implies that each corner of the square will touch the circumference of the circle. To achieve this, one must follow several geometric construction steps using a compass and straightedge. As the question contains what appears to be step descriptions but with some typos and inconsistencies, we will assume the goal is to properly order these steps to successfully inscribe a square within a circle. The correct sequence of steps to construct an inscribed square should allow us to use the circle's diameter to determine the side length of the square and ensure that its vertices lie on the circle.

Looking at the steps provided, Step M should indeed be the first step. You place the compass at the endpoint of the diameter and construct an arc that crosses the circle. This helps to determine the perpendicular bisector of the diameter, which is essential for locating the points where the square will touch the circle. Next, Step N involves drawing two diameters to find the points intersecting the arc, which are two opposite vertices of the square. Step O generates another arc that intersects the circle at two more points, which are the remaining vertices of the square. Step P involves drawing a line segment between these two new points, and finally, Step Q is about connecting all four vertices with line segments, resulting in a square.

Therefore, the correct order of steps to construct a square inscribed in a circle is M, N, O, P, Q, which corresponds to option a).