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The diameter of the circumcircle of a square is the diameter of the circle that passes through all four vertices of the square. It represents the longest distance between any two points on the circumcircle and is directly related to the square's geometry.
The calculator uses the formula:
Where:
Explanation: This formula establishes the relationship between the inradius (radius of the inscribed circle) and the diameter of the circumscribed circle of a square. The factor \( 2\sqrt{2} \) comes from the geometric properties of squares.
Details: Calculating the circumcircle diameter is important in various geometric applications, construction projects, and engineering designs where circular elements need to accommodate square components or vice versa.
Tips: Enter the inradius of the square in meters. The value must be positive and greater than zero. The calculator will compute the corresponding diameter of the circumcircle.
Q1: What is the relationship between inradius and circumcircle diameter?
A: The diameter of the circumcircle is exactly \( 2\sqrt{2} \) times the inradius of the square.
Q2: Can this formula be used for rectangles?
A: No, this specific formula applies only to squares. Rectangles have different geometric relationships between their incircle and circumcircle.
Q3: What are typical applications of this calculation?
A: This calculation is used in mechanical engineering, architecture, woodworking, and any field where square components need to fit within circular boundaries.
Q4: How accurate is this formula?
A: The formula is mathematically exact and provides perfect accuracy for ideal squares.
Q5: Can I calculate inradius from circumcircle diameter?
A: Yes, the formula can be rearranged as \( r_i = \frac{D_c}{2\sqrt{2}} \) to find the inradius from the circumcircle diameter.