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Circumradius of Decagon given Diagonal across Two Sides 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 d 2}{\sqrt{10 + (2 \cdot \sqrt{5})}}

r_c - Circumradius of Decagon?d₂ - Diagonal across Two Sides of Decagon?

Circumradius of Decagon given Diagonal across Two Sides Example

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Here is how the Circumradius of Decagon given Diagonal across Two Sides equation looks like with Values.

Here is how the Circumradius of Decagon given Diagonal across Two Sides equation looks like with Units.

Here is how the Circumradius of Decagon given Diagonal across Two Sides equation looks like.

16.1624 = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

16.1624m = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

16.1624 = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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Circumradius of Decagon given Diagonal across Two Sides Solution

Follow our step by step solution on how to calculate Circumradius of Decagon given Diagonal across Two Sides?

FIRST Step Consider the formula

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot d 2}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r c = 16.1623653586888m

LAST Step Rounding Answer

∴

r c = 16.1624m

Circumradius of Decagon given Diagonal across Two Sides 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

Diagonal across Two Sides of Decagon

Diagonal across Two Sides of Decagon is a straight line joining two non-adjacent sides which is across two sides of the Decagon.

Symbol: d₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Two Sides 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 Diagonal across Two Sides?

Circumradius of Decagon given Diagonal across Two Sides evaluator uses Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5))) to evaluate the Circumradius of Decagon, The Circumradius of Decagon given Diagonal across Two Sides 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 a diagonal across two sides. Circumradius of Decagon is denoted by r_c symbol.

How to evaluate Circumradius of Decagon given Diagonal across Two Sides using this online evaluator? To use this online evaluator for Circumradius of Decagon given Diagonal across Two Sides, enter Diagonal across Two Sides of Decagon (d₂) and hit the calculate button.

FAQs on Circumradius of Decagon given Diagonal across Two Sides

What is the formula to find Circumradius of Decagon given Diagonal across Two Sides?

The formula of Circumradius of Decagon given Diagonal across Two Sides is expressed as Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5))). Here is an example- 16.16237 = (1+sqrt(5))/2*(2*19)/sqrt(10+(2*sqrt(5))).

How to calculate Circumradius of Decagon given Diagonal across Two Sides?

With Diagonal across Two Sides of Decagon (d₂) we can find Circumradius of Decagon given Diagonal across Two Sides using the formula - Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(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 Diagonal across Two Sides be negative?

No, the Circumradius of Decagon given Diagonal across Two Sides, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Decagon given Diagonal across Two Sides?

Circumradius of Decagon given Diagonal across Two Sides 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 Diagonal across Two Sides can be measured.

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