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Circumradius of Decagon given Inradius Formula

GoCircumradius of Decagon given Width Formula

GoCircumradius of Decagon given Diagonal across Five Sides Formula

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Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices. Check FAQs

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot r i}{\sqrt{5 + (2 \cdot \sqrt{5})}}

r_c - Circumradius of Decagon?r_i - Inradius of Decagon?

Circumradius of Decagon given Inradius Example

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

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

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

15.7719 = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

15.7719m = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

15.7719 = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Circumradius of Decagon given Inradius Solution

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

FIRST Step Consider the formula

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot r i}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r c = 15.771933363574m

LAST Step Rounding Answer

∴

r c = 15.7719m

Circumradius of Decagon given Inradius Formula Elements

Variables

Functions

Circumradius of Decagon

Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Decagon

Inradius of Decagon

Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Decagon

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 Circumradius of Decagon

Go Circumradius of Decagon given Width

r c = \frac{w}{2}

Go Circumradius of Decagon given Diagonal across Five Sides

r c = \frac{d 5}{2}

Go Circumradius of Decagon given Diagonal across Four Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{d 4}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Go Circumradius of Decagon given Diagonal across Three Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}}

How to Evaluate Circumradius of Decagon given Inradius?

Circumradius of Decagon given Inradius evaluator uses Circumradius of Decagon = (1+sqrt(5))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))) to evaluate the Circumradius of Decagon, The Circumradius of Decagon given Inradius formula is defined as a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using its inradius. Circumradius of Decagon is denoted by r_c symbol.

How to evaluate Circumradius of Decagon given Inradius using this online evaluator? To use this online evaluator for Circumradius of Decagon given Inradius, enter Inradius of Decagon (r_i) and hit the calculate button.

FAQs on Circumradius of Decagon given Inradius

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

The formula of Circumradius of Decagon given Inradius is expressed as Circumradius of Decagon = (1+sqrt(5))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). Here is an example- 15.77193 = (1+sqrt(5))/2*(2*15)/sqrt(5+(2*sqrt(5))).

How to calculate Circumradius of Decagon given Inradius?

With Inradius of Decagon (r_i) we can find Circumradius of Decagon given Inradius using the formula - Circumradius of Decagon = (1+sqrt(5))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Decagon?

Here are the different ways to Calculate Circumradius of Decagon-

Circumradius of Decagon=Width of Decagon/2
Circumradius of Decagon=Diagonal across Five Sides of Decagon/2
Circumradius of Decagon=(1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

Can the Circumradius of Decagon given Inradius be negative?

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

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

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

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