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Inradius of Dodecagon given Circumradius Formula

GoInradius of Dodecagon given Diagonal across Two Sides Formula

GoInradius of Dodecagon given Diagonal across Three Sides Formula

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Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon. Check FAQs

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{r c}{\frac{\sqrt{6} + \sqrt{2}}{2}}

r_i - Inradius of Dodecagon?r_c - Circumradius of Dodecagon?

Inradius of Dodecagon given Circumradius Example

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Here is how the Inradius of Dodecagon given Circumradius equation looks like with Values.

Here is how the Inradius of Dodecagon given Circumradius equation looks like with Units.

Here is how the Inradius of Dodecagon given Circumradius equation looks like.

19.3185 = \frac{2 + \sqrt{3}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

19.3185m = \frac{2 + \sqrt{3}}{2} \cdot \frac{20m}{\frac{\sqrt{6} + \sqrt{2}}{2}}

19.3185 = \frac{2 + \sqrt{3}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

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Inradius of Dodecagon given Circumradius Solution

Follow our step by step solution on how to calculate Inradius of Dodecagon given Circumradius?

FIRST Step Consider the formula

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{r c}{\frac{\sqrt{6} + \sqrt{2}}{2}}

Next Step Substitute values of Variables

∴

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{20m}{\frac{\sqrt{6} + \sqrt{2}}{2}}

Next Step Prepare to Evaluate

∴

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

Next Step Evaluate

∴

r i = 19.3185165257814m

LAST Step Rounding Answer

∴

r i = 19.3185m

Inradius of Dodecagon given Circumradius Formula Elements

Variables

Functions

Inradius of Dodecagon

Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Dodecagon

Circumradius of Dodecagon

Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Dodecagon

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.

Syntax: sqrt(Number)

Other Formulas to find Inradius of Dodecagon

Go Inradius of Dodecagon given Diagonal across Two Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 2}{\frac{\sqrt{2} + \sqrt{6}}{2}}

Go Inradius of Dodecagon given Diagonal across Three Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 3}{\sqrt{3} + 1}

Go Inradius of Dodecagon given Diagonal across Four Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 4}{\frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2}}

Go Inradius of Dodecagon given Diagonal across Six Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 6}{\sqrt{6} + \sqrt{2}}

How to Evaluate Inradius of Dodecagon given Circumradius?

Inradius of Dodecagon given Circumradius evaluator uses Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2) to evaluate 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 evaluate Inradius of Dodecagon given Circumradius using this online evaluator? To use this online evaluator for Inradius of Dodecagon given Circumradius, enter Circumradius of Dodecagon (r_c) and hit the calculate button.

FAQs on Inradius of Dodecagon given Circumradius

What is the formula to find Inradius of Dodecagon given Circumradius?

The formula of Inradius of Dodecagon given Circumradius is expressed as Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). Here is an example- 19.31852 = (2+sqrt(3))/2*20/((sqrt(6)+sqrt(2))/2).

How to calculate Inradius of Dodecagon given Circumradius?

With Circumradius of Dodecagon (r_c) we can find Inradius of Dodecagon given Circumradius using the formula - Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Dodecagon?

Here are the different ways to Calculate Inradius of Dodecagon-

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)

Can the Inradius of Dodecagon given Circumradius be negative?

No, the Inradius of Dodecagon given Circumradius, measured in Length cannot be negative.

Which unit is used to measure Inradius of Dodecagon given Circumradius?

Inradius of Dodecagon given Circumradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Dodecagon given Circumradius can be measured.

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