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Circumradius of Octagon given inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
rc = (((2*ri)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Inradius - Inradius is defined as the radius of the circle which is inscribed inside the polygon. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Inradius: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (((2*ri)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) --> (((2*10)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
Evaluating ... ...
rc = 10.8239220029239
STEP 3: Convert Result to Output's Unit
10.8239220029239 Meter --> No Conversion Required
FINAL ANSWER
10.8239220029239 Meter <-- Circumradius
(Calculation completed in 00.015 seconds)

9 Circumradius of Octagon Calculators

Circumradius of Octagon given short diagonal
circumradius = (((Short diagonal/(sqrt(2+sqrt(2)))))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given area
circumradius = ((sqrt(Area/(2*(1+sqrt(2)))))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given medium diagonal
circumradius = ((Medium diagonal/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given long diagonal
circumradius = ((Long diagonal/(4+2*sqrt(2)))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given inradius
circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given height
circumradius = ((Height/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given perimeter
circumradius = ((Perimeter/8)/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon
circumradius = (Side/2)*sqrt(4+2*sqrt(2)) Go
Circumradius of Octagon given side and angle
circumradius = Side/(2*sin(Angle A/2)) Go

Circumradius of Octagon given inradius Formula

circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
rc = (((2*ri)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))

What is an octagon?

Octagon is a polygon with eight sides and eight vertices. An octagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. A convex octagon has none of its interior angles greater than 180°. To the contrary, a concave octagon (or polygon) has one or more of its interior angles greater than 180°

How to Calculate Circumradius of Octagon given inradius?

Circumradius of Octagon given inradius calculator uses circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) to calculate the Circumradius, The Circumradius of Octagon given inradius formula is defined as straight line from the centre to the circumference of an octagon, where radius= radius of octagon Rc=1.307*a where a is side and Rc is circumradius of octagon. Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Octagon given inradius using this online calculator? To use this online calculator for Circumradius of Octagon given inradius, enter Inradius (ri) and hit the calculate button. Here is how the Circumradius of Octagon given inradius calculation can be explained with given input values -> 10.82392 = (((2*10)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)).

FAQ

What is Circumradius of Octagon given inradius?
The Circumradius of Octagon given inradius formula is defined as straight line from the centre to the circumference of an octagon, where radius= radius of octagon Rc=1.307*a where a is side and Rc is circumradius of octagon and is represented as rc = (((2*ri)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)) or circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)). Inradius is defined as the radius of the circle which is inscribed inside the polygon.
How to calculate Circumradius of Octagon given inradius?
The Circumradius of Octagon given inradius formula is defined as straight line from the centre to the circumference of an octagon, where radius= radius of octagon Rc=1.307*a where a is side and Rc is circumradius of octagon is calculated using circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2)). To calculate Circumradius of Octagon given inradius, you need Inradius (ri). With our tool, you need to enter the respective value for Inradius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Circumradius?
In this formula, Circumradius uses Inradius. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • circumradius = Side/(2*sin(Angle A/2))
  • circumradius = (Side/2)*sqrt(4+2*sqrt(2))
  • circumradius = ((Long diagonal/(4+2*sqrt(2)))/2)*sqrt(4+2*sqrt(2))
  • circumradius = ((Medium diagonal/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
  • circumradius = (((Short diagonal/(sqrt(2+sqrt(2)))))/2)*sqrt(4+2*sqrt(2))
  • circumradius = ((Height/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
  • circumradius = ((Perimeter/8)/2)*sqrt(4+2*sqrt(2))
  • circumradius = ((sqrt(Area/(2*(1+sqrt(2)))))/2)*sqrt(4+2*sqrt(2))
  • circumradius = (((2*Inradius)/(1+sqrt(2)))/2)*sqrt(4+2*sqrt(2))
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