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Circumradius of Hexadecagon given Inradius Formula

GoCircumradius of Hexadecagon given Diagonal across Eight Sides Formula

GoCircumradius of Hexadecagon Formula

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

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{r i}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

r_c - Circumradius of Hexadecagon?r_i - Inradius of Hexadecagon?

Circumradius of Hexadecagon given Inradius Example

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

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

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

12.2351 = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{12}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

12.2351m = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{12m}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

12.2351 = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{12}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

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Circumradius of Hexadecagon given Inradius Solution

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

FIRST Step Consider the formula

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{r i}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

Next Step Substitute values of Variables

∴

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{12m}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

Next Step Prepare to Evaluate

∴

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot (\frac{12}{\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}})

Next Step Evaluate

∴

r c = 12.2350938984998m

LAST Step Rounding Answer

∴

r c = 12.2351m

Circumradius of Hexadecagon given Inradius Formula Elements

Variables

Functions

Circumradius of Hexadecagon

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Hexadecagon

Inradius of Hexadecagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Hexadecagon

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 Hexadecagon

Go Circumradius of Hexadecagon given Diagonal across Eight Sides

r c = \frac{d 8}{2}

Go Circumradius of Hexadecagon

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot S

Go Circumradius of Hexadecagon given Diagonal across Seven Sides

r c = \frac{d 7 \cdot \sin (\frac{π}{16})}{\sin (\frac{7 \cdot π}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Go Circumradius of Hexadecagon given Diagonal across Six Sides

r c = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

How to Evaluate Circumradius of Hexadecagon given Inradius?

Circumradius of Hexadecagon given Inradius evaluator uses Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) to evaluate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using inradius. Circumradius of Hexadecagon is denoted by r_c symbol.

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

FAQs on Circumradius of Hexadecagon given Inradius

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

The formula of Circumradius of Hexadecagon given Inradius is expressed as Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)). Here is an example- 12.23509 = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)).

How to calculate Circumradius of Hexadecagon given Inradius?

With Inradius of Hexadecagon (r_i) we can find Circumradius of Hexadecagon given Inradius using the formula - Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Hexadecagon?

Here are the different ways to Calculate Circumradius of Hexadecagon-

Circumradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon/2
Circumradius of Hexadecagon=sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon
Circumradius of Hexadecagon=(Diagonal across Seven Sides of Hexadecagon*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Can the Circumradius of Hexadecagon given Inradius be negative?

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

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

Circumradius of Hexadecagon 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 Hexadecagon given Inradius can be measured.

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