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The circumradius of an octagon is the radius of the circumscribed circle that passes through all vertices of the octagon. Given the inradius (radius of the inscribed circle), this calculator computes the circumradius using the mathematical relationship between these two properties of a regular octagon.
The calculator uses the formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the circumradius and inradius of a regular octagon, derived from geometric properties of the shape.
Details: Calculating the circumradius is essential in various geometric applications, architectural designs, and engineering projects involving octagonal structures. It helps determine the spatial requirements and relationships between inscribed and circumscribed circles.
Tips: Enter the inradius value in meters. The value must be a positive number greater than zero. The calculator will compute the corresponding circumradius based on the geometric relationship.
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 circumradius related to the side length?
A: For a regular octagon with side length s, the circumradius \( r_c = \frac{s}{2} \times \sqrt{4 + 2\sqrt{2}} \).
Q3: Can this calculator be used for irregular octagons?
A: No, this calculator is specifically designed for regular octagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is useful in architecture, engineering, and design projects involving octagonal structures, such as buildings, towers, or mechanical components.
Q5: How accurate is the formula?
A: The formula is mathematically exact for regular octagons and provides precise results when accurate input values are provided.