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Circumradius of Pentagon given Inradius using Interior Angle Formula

GoCircumradius of Pentagon given Edge Length using Central Angle Formula

GoCircumradius of Pentagon given Inradius Formula

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The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon. Check FAQs

r c = \frac{r i}{\frac{1}{2} - \cos (\frac{3}{5} \cdot π)}

r_c - Circumradius of Pentagon?r_i - Inradius of Pentagon?π - Archimedes' constant?

Circumradius of Pentagon given Inradius using Interior Angle Example

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Here is how the Circumradius of Pentagon given Inradius using Interior Angle equation looks like with Values.

Here is how the Circumradius of Pentagon given Inradius using Interior Angle equation looks like with Units.

Here is how the Circumradius of Pentagon given Inradius using Interior Angle equation looks like.

8.6525 = \frac{7}{\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416)}

8.6525m = \frac{7m}{\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416)}

8.6525 = \frac{7}{\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416)}

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Circumradius of Pentagon given Inradius using Interior Angle Solution

Follow our step by step solution on how to calculate Circumradius of Pentagon given Inradius using Interior Angle?

FIRST Step Consider the formula

r c = \frac{r i}{\frac{1}{2} - \cos (\frac{3}{5} \cdot π)}

Next Step Substitute values of Variables

∴

r c = \frac{7m}{\frac{1}{2} - \cos (\frac{3}{5} \cdot π)}

Next Step Substitute values of Constants

∴

r c = \frac{7m}{\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416)}

Next Step Prepare to Evaluate

∴

r c = \frac{7}{\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416)}

Next Step Evaluate

∴

r c = 8.65247584249853m

LAST Step Rounding Answer

∴

r c = 8.6525m

Circumradius of Pentagon given Inradius using Interior Angle Formula Elements

Variables

Constants

Functions

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Pentagon

Inradius of Pentagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Circumradius of Pentagon

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon given Inradius

r c = \frac{r i}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Inradius using Central Angle

r c = \frac{r i}{\cos (\frac{π}{5})}

How to Evaluate Circumradius of Pentagon given Inradius using Interior Angle?

Circumradius of Pentagon given Inradius using Interior Angle evaluator uses Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)) to evaluate the Circumradius of Pentagon, The Circumradius of Pentagon given Inradius using Interior Angle is defined as the length of the line joining the center and a point on the circumcircle of the Pentagon, calculated using inradius and interior angle. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQs on Circumradius of Pentagon given Inradius using Interior Angle

What is the formula to find Circumradius of Pentagon given Inradius using Interior Angle?

The formula of Circumradius of Pentagon given Inradius using Interior Angle is expressed as Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)). Here is an example- 8.652476 = 7/(1/2-cos(3/5*pi)).

How to calculate Circumradius of Pentagon given Inradius using Interior Angle?

With Inradius of Pentagon (r_i) we can find Circumradius of Pentagon given Inradius using Interior Angle using the formula - Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Circumradius of Pentagon?

Here are the different ways to Calculate Circumradius of Pentagon-

Circumradius of Pentagon=(Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon=(Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))
Circumradius of Pentagon=Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))

Can the Circumradius of Pentagon given Inradius using Interior Angle be negative?

No, the Circumradius of Pentagon given Inradius using Interior Angle, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Pentagon given Inradius using Interior Angle?

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

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