Question

given the circle centered at point a, construct a square inscribed in the circle. explain your steps.

1. given square abcd, construct a circle circumscribed about the square. explain your steps.

Explanation:

Step1: Draw the diagonals

Draw diagonals AC and BD of square ABCD. The diagonals of a square are equal in length, bisect each other, and are perpendicular. The intersection point of the diagonals is the center of the circum - circle. Let the intersection point be O.

Step2: Set the compass

Set the compass width to the distance from O to any vertex of the square (e.g., OA, OB, OC, or OD). Since the diagonals of a square bisect each other, OA = OB = OC = OD.

Step3: Draw the circle

With the compass centered at O and the set width, draw a circle. This circle will pass through all four vertices A, B, C, and D of the square, and it is the circum - circle of the square ABCD.

Answer:

Follow the above - described three - step construction process to draw the circle circumscribed about square ABCD.