Circumradius of Hexadecagon given Inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
rc = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
Inradius of Hexadecagon - (Measured in Meter) - Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.
STEP 1: Convert Input(s) to Base Unit
Inradius of Hexadecagon: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) --> (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))
Evaluating ... ...
rc = 12.2350938984998
STEP 3: Convert Result to Output's Unit
12.2350938984998 Meter --> No Conversion Required
FINAL ANSWER
12.2350938984998 Meter <-- Circumradius of Hexadecagon
(Calculation completed in 00.013 seconds)

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10+ Circumradius of Hexadecagon Calculators

Circumradius of Hexadecagon given Diagonal across Seven Sides
Circumradius of Hexadecagon = Diagonal across Seven Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(7*pi/16)/sin(pi/16)) Go
Circumradius of Hexadecagon given Diagonal across Three Sides
Circumradius of Hexadecagon = Diagonal across Three Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(3*pi/16)/sin(pi/16)) Go
Circumradius of Hexadecagon given Diagonal across Five Sides
Circumradius of Hexadecagon = Diagonal across Five Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(5*pi/16)/sin(pi/16)) Go
Circumradius of Hexadecagon given Diagonal across Six Sides
Circumradius of Hexadecagon = Diagonal across Six Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(3*pi/8)/sin(pi/16)) Go
Circumradius of Hexadecagon given Diagonal across Two Sides
Circumradius of Hexadecagon = Diagonal across Two Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(pi/8)/sin(pi/16)) Go
Circumradius of Hexadecagon given Diagonal across Four Sides
Circumradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sqrt(2)/2/(sin(pi/16))) Go
Circumradius of Hexadecagon given Area
Circumradius of Hexadecagon = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(sqrt((Area of Hexadecagon)/(4*cot(pi/16)))) Go
Circumradius of Hexadecagon given Perimeter
Circumradius of Hexadecagon = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(Perimeter of Hexadecagon/16) Go
Circumradius of Hexadecagon
Circumradius of Hexadecagon = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*Side of Hexadecagon Go
Circumradius of Hexadecagon given Diagonal across Eight Sides
Circumradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon/2 Go

Circumradius of Hexadecagon given Inradius 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))
rc = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))

What is Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture.

How to Calculate Circumradius of Hexadecagon given Inradius?

Circumradius of Hexadecagon given Inradius calculator 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 calculate 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 rc symbol.

How to calculate Circumradius of Hexadecagon given Inradius using this online calculator? To use this online calculator for Circumradius of Hexadecagon given Inradius, enter Inradius of Hexadecagon (ri) and hit the calculate button. Here is how the Circumradius of Hexadecagon given Inradius calculation can be explained with given input values -> 12.23509 = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)).

FAQ

What is Circumradius of Hexadecagon given Inradius?
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 and is represented as rc = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) or 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)). Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.
How to calculate Circumradius of Hexadecagon given Inradius?
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 is calculated using 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 calculate Circumradius of Hexadecagon given Inradius, you need Inradius of Hexadecagon (ri). With our tool, you need to enter the respective value for Inradius of Hexadecagon 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 of Hexadecagon?
In this formula, Circumradius of Hexadecagon uses Inradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • 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*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(7*pi/16)/sin(pi/16))
  • Circumradius of Hexadecagon = Diagonal across Six Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(3*pi/8)/sin(pi/16))
  • Circumradius of Hexadecagon = Diagonal across Five Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(5*pi/16)/sin(pi/16))
  • Circumradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sqrt(2)/2/(sin(pi/16)))
  • Circumradius of Hexadecagon = Diagonal across Three Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(3*pi/16)/sin(pi/16))
  • Circumradius of Hexadecagon = Diagonal across Two Sides of Hexadecagon*(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))/(sin(pi/8)/sin(pi/16))
  • Circumradius of Hexadecagon = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(sqrt((Area of Hexadecagon)/(4*cot(pi/16))))
  • Circumradius of Hexadecagon = (sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*(Perimeter of Hexadecagon/16)
  • Circumradius of Hexadecagon = ((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))*(Height of Hexadecagon/(sin(7*pi/16)/sin(pi/16)))
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