Circumradius of Dodecagon given Inradius Calculator

✖Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.ⓘ Circumradius of Dodecagon given Inradius [r_c]

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Formula

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Circumradius of Dodecagon given Inradius

Formula

`"r"_{"c"} = (sqrt(6)+sqrt(2))/2*"r"_{"i"}/((2+sqrt(3))/2)`

Example

`"19.67025m"=(sqrt(6)+sqrt(2))/2*"19m"/((2+sqrt(3))/2)`

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Circumradius of Dodecagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2)
r_c = (sqrt(6)+sqrt(2))/2*r_i/((2+sqrt(3))/2)
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Circumradius of Dodecagon - (Measured in Meter) - Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.
Inradius of Dodecagon - (Measured in Meter) - Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Dodecagon: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (sqrt(6)+sqrt(2))/2*r_i/((2+sqrt(3))/2) --> (sqrt(6)+sqrt(2))/2*19/((2+sqrt(3))/2)

Evaluating ... ...

r_c = 19.6702474277916

STEP 3: Convert Result to Output's Unit

19.6702474277916 Meter --> No Conversion Required

FINAL ANSWER

19.6702474277916 ≈ 19.67025 Meter <-- Circumradius of Dodecagon

(Calculation completed in 00.021 seconds)

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< 11 Circumradius of Dodecagon Calculators

Circumradius of Dodecagon given Diagonal across Four Sides

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)

Circumradius of Dodecagon given Area

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))

Circumradius of Dodecagon given Diagonal across Five Sides

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3))

Circumradius of Dodecagon given Inradius

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2)

Circumradius of Dodecagon given Height

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))

Circumradius of Dodecagon given Width

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Width of Dodecagon/(2+sqrt(3))

Circumradius of Dodecagon given Perimeter

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/24*Perimeter of Dodecagon

Circumradius of Dodecagon

Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Side of Dodecagon

Circumradius of Dodecagon given Diagonal across Three Sides

Go Circumradius of Dodecagon = Diagonal Across Three Sides of Dodecagon/sqrt(2)

Circumradius of Dodecagon given Diagonal across Six Sides

Go Circumradius of Dodecagon = Diagonal Across Six Sides of Dodecagon/2

Circumradius of Dodecagon given Diagonal across Two Sides

Go Circumradius of Dodecagon = Diagonal Across Two Sides of Dodecagon/1

Circumradius of Dodecagon given Inradius Formula

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2)
r_c = (sqrt(6)+sqrt(2))/2*r_i/((2+sqrt(3))/2)

What is Dodecagon?

A regular Dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational symmetry of order 12. It can be constructed as a truncated hexagon, t{6}, or a twice-truncated triangle, tt{3}. The internal angle at each vertex of a regular dodecagon is 150°.

How to Calculate Circumradius of Dodecagon given Inradius?

Circumradius of Dodecagon given Inradius calculator uses Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2) to calculate the Circumradius of Dodecagon, The Circumradius of Dodecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circumcircle that touches all vertices of the Dodecagon, calculated using inradius. Circumradius of Dodecagon is denoted by r_c symbol.

How to calculate Circumradius of Dodecagon given Inradius using this online calculator? To use this online calculator for Circumradius of Dodecagon given Inradius, enter Inradius of Dodecagon (r_i) and hit the calculate button. Here is how the Circumradius of Dodecagon given Inradius calculation can be explained with given input values -> 19.67025 = (sqrt(6)+sqrt(2))/2*19/((2+sqrt(3))/2).

FAQ

What is Circumradius of Dodecagon given Inradius?

The Circumradius of Dodecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circumcircle that touches all vertices of the Dodecagon, calculated using inradius and is represented as r_c = (sqrt(6)+sqrt(2))/2*r_i/((2+sqrt(3))/2) or Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2). Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

How to calculate Circumradius of Dodecagon given Inradius?

The Circumradius of Dodecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circumcircle that touches all vertices of the Dodecagon, calculated using inradius is calculated using Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2). To calculate Circumradius of Dodecagon given Inradius, you need Inradius of Dodecagon (r_i). With our tool, you need to enter the respective value for Inradius of Dodecagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Circumradius of Dodecagon?

In this formula, Circumradius of Dodecagon uses Inradius of Dodecagon. We can use 10 other way(s) to calculate the same, which is/are as follows -

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Side of Dodecagon
Circumradius of Dodecagon = Diagonal Across Six Sides of Dodecagon/2
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3))
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)
Circumradius of Dodecagon = Diagonal Across Three Sides of Dodecagon/sqrt(2)
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/24*Perimeter of Dodecagon
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))
Circumradius of Dodecagon = Diagonal Across Two Sides of Dodecagon/1
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Width of Dodecagon/(2+sqrt(3))

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