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The Circumradius of Octagon is the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle. It represents the distance from the center of the octagon to any of its vertices.
The calculator uses the formula:
Where:
Explanation: The circumradius of a regular octagon is exactly half the length of its longest diagonal. This relationship holds true for all regular octagons due to their symmetrical properties.
Details: Calculating the circumradius is essential in geometry, architecture, and engineering applications involving octagonal shapes. It helps determine the size of the circumscribed circle and is crucial for various design and construction purposes.
Tips: Enter the long diagonal measurement in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all interior angles are equal (135 degrees each).
Q2: How is the long diagonal different from other diagonals?
A: The long diagonal connects opposite vertices of the octagon and is the longest possible diagonal, passing through the center of the octagon.
Q3: Can this formula be used for irregular octagons?
A: No, this formula applies only to regular octagons where all sides and angles are equal. Irregular octagons do not have a consistent circumradius.
Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, engineering projects, manufacturing of octagonal components, and various geometric constructions.
Q5: How does the circumradius relate to the side length?
A: For a regular octagon, the circumradius can also be calculated from the side length using the formula: \( r_c = s \times \sqrt{\frac{4 + 2\sqrt{2}}{2}} \), where s is the side length.