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The Circumradius of a Dodecagon is the radius of a circumcircle touching each of the vertices of the Dodecagon. It represents the distance from the center of the dodecagon to any of its vertices when the dodecagon is inscribed in a circle.
The calculator uses the formula:
Where:
Explanation: The circumradius is exactly half the length of the diagonal that spans across six sides of the dodecagon.
Details: Calculating the circumradius is essential in geometry for determining the properties of regular polygons, designing circular patterns, and solving problems related to polygon circumscription.
Tips: Enter the diagonal across six sides of the dodecagon in meters. The value must be positive and greater than zero.
Q1: What is a Dodecagon?
A: A dodecagon is a polygon with twelve sides and twelve angles. A regular dodecagon has all sides equal and all interior angles equal.
Q2: What is the relationship between circumradius and side length?
A: For a regular dodecagon, the circumradius \( r_c \) is related to the side length \( s \) by the formula: \( r_c = \frac{s}{2} \cdot \frac{\sqrt{6} + \sqrt{2}}{2} \).
Q3: Can this formula be used for irregular dodecagons?
A: No, this specific formula applies only to regular dodecagons where all sides and angles are equal.
Q4: What are practical applications of dodecagon geometry?
A: Dodecagons are used in architecture, coin design, clock faces, and various decorative patterns where symmetrical twelve-sided shapes are desired.
Q5: How does the circumradius relate to the incircle radius?
A: For a regular dodecagon, the circumradius is larger than the inradius (the radius of the inscribed circle), with a specific mathematical relationship between them.