Constructing a Square Inscribed in a Circle Construct a square with vertex A inscribed in the given circle. Undo
The Correct Answer and Explanation is:
To construct a square inscribed in a given circle with vertex A, follow these steps carefully:
- Identify the center of the circle and label it as C. The given vertex A lies on the circumference.
- Draw a diameter of the circle that passes through point A. Label the other intersection point as B.
- Using a compass, place the pivot at C and draw a perpendicular diameter to AB. Label its intersection points with the circle as D and E.
- Connect points A, B, D, and E in sequence to form the square.
Explanation
This geometric construction ensures that all four vertices of the square lie on the circle. The key idea is utilizing perpendicular diameters. When constructing the square, the first step is drawing the diameter AB, which establishes a foundational reference. The second diameter, perpendicular to AB, guarantees a ninety-degree angle at intersection points D and E.
By connecting A to D, D to B, B to E, and E back to A, a quadrilateral is formed. Since all sides are equal and angles are precisely ninety degrees, the figure is a square. The circle serves as the circumcircle of the square, ensuring all vertices are equidistant from its center.
This construction is valuable in applications such as engineering and design, where geometric precision is necessary. Understanding inscribed figures helps in spatial reasoning, influencing fields like architecture and mechanical design. The method relies purely on fundamental geometric principles, making it a practical approach that eliminates complex calculations. With precise execution, the square fits neatly within the circle while adhering to mathematical accuracy.
