Inradius of Dodecagon given Circumradius Calculator

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

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✖Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.ⓘ Inradius of Dodecagon given Circumradius [r_i]

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Inradius of Dodecagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Circumradius of Dodecagon: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (2+sqrt(3))/2*r_c/((sqrt(6)+sqrt(2))/2) --> (2+sqrt(3))/2*20/((sqrt(6)+sqrt(2))/2)

Evaluating ... ...

r_i = 19.3185165257814

STEP 3: Convert Result to Output's Unit

19.3185165257814 Meter --> No Conversion Required

FINAL ANSWER

19.3185165257814 ≈ 19.31852 Meter <-- Inradius of Dodecagon

(Calculation completed in 00.020 seconds)

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< Inradius of Dodecagon Calculators

Inradius of Dodecagon given Diagonal across Four Sides

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

Inradius of Dodecagon given Diagonal across Two Sides

LaTeX Go Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)

Inradius of Dodecagon given Diagonal across Six Sides

LaTeX Go Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Six Sides of Dodecagon/(sqrt(6)+sqrt(2))

Inradius of Dodecagon given Diagonal across Three Sides

LaTeX Go Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1)

Inradius of Dodecagon given Circumradius Formula

LaTeX Go

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

Inradius of Dodecagon given Circumradius calculator uses Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2) to calculate the Inradius of Dodecagon, The Inradius of Dodecagon given Circumradius formula is defined as the line connecting the incenter and any point on the incircle that touches all the edges of the Dodecagon, calculated using circumradius. Inradius of Dodecagon is denoted by r_i symbol.

How to calculate Inradius of Dodecagon given Circumradius using this online calculator? To use this online calculator for Inradius of Dodecagon given Circumradius, enter Circumradius of Dodecagon (r_c) and hit the calculate button. Here is how the Inradius of Dodecagon given Circumradius calculation can be explained with given input values -> 19.31852 = (2+sqrt(3))/2*20/((sqrt(6)+sqrt(2))/2).

FAQ

What is Inradius of Dodecagon given Circumradius?

The Inradius of Dodecagon given Circumradius formula is defined as the line connecting the incenter and any point on the incircle that touches all the edges of the Dodecagon, calculated using circumradius and is represented as r_i = (2+sqrt(3))/2*r_c/((sqrt(6)+sqrt(2))/2) or Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

How to calculate Inradius of Dodecagon given Circumradius?

The Inradius of Dodecagon given Circumradius formula is defined as the line connecting the incenter and any point on the incircle that touches all the edges of the Dodecagon, calculated using circumradius is calculated using Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). To calculate Inradius of Dodecagon given Circumradius, you need Circumradius of Dodecagon (r_c). With our tool, you need to enter the respective value for Circumradius 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 Inradius of Dodecagon?

In this formula, Inradius of Dodecagon uses Circumradius of Dodecagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)
Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1)
Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)

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