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Circumradius of Pentagon given inradius and central angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = (Inradius)/(cos(Central Angle/2))
rc = (ri)/(cos(Anglecentral/2))
This formula uses 1 Functions, 2 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Inradius - Inradius is defined as the radius of the circle which is inscribed inside the polygon. (Measured in Meter)
Central Angle - A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Inradius: 10 Meter --> 10 Meter No Conversion Required
Central Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (ri)/(cos(Anglecentral/2)) --> (10)/(cos(0.785398163397301/2))
Evaluating ... ...
rc = 10.8239220029236
STEP 3: Convert Result to Output's Unit
10.8239220029236 Meter --> No Conversion Required
FINAL ANSWER
10.8239220029236 Meter <-- Circumradius
(Calculation completed in 00.016 seconds)

8 Circumradius of Pentagon Calculators

Circumradius of Pentagon given height and central angle
circumradius = (Height)/(1+cos(Central Angle/2)) Go
Circumradius of Pentagon given inradius and central angle
circumradius = (Inradius)/(cos(Central Angle/2)) Go
Circumradius of Pentagon given side and central angle
circumradius = (Side)/(2*sin(Central Angle/2)) Go
Circumradius of Pentagon given height and inradius
circumradius = Height-Inradius Go
Circumradius of Pentagon given inradius
circumradius = (Inradius/0.809) Go
Circumradius of Pentagon given diagonal
circumradius = 0.5257*Diagonal Go
Circumradius of Pentagon given height
circumradius = (Height/1.809) Go
Circumradius of Pentagon given side
circumradius = (0.851*Side) Go

Circumradius of Pentagon given inradius and central angle Formula

circumradius = (Inradius)/(cos(Central Angle/2))
rc = (ri)/(cos(Anglecentral/2))

What is circumcircle of pentagon?

A circle that passes through all the five vertices of the regular pentagon . This is the so called circumscribed circle or circumcircle of the regular pentagon.

How to Calculate Circumradius of Pentagon given inradius and central angle?

Circumradius of Pentagon given inradius and central angle calculator uses circumradius = (Inradius)/(cos(Central Angle/2)) to calculate the Circumradius, Circumradius of Pentagon given inradius and central angle is defined as the line joining the center and one point on circumcircle of pentagon. Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Pentagon given inradius and central angle using this online calculator? To use this online calculator for Circumradius of Pentagon given inradius and central angle, enter Inradius (ri) & Central Angle (Anglecentral) and hit the calculate button. Here is how the Circumradius of Pentagon given inradius and central angle calculation can be explained with given input values -> 10.82392 = (10)/(cos(0.785398163397301/2)).

FAQ

What is Circumradius of Pentagon given inradius and central angle?
Circumradius of Pentagon given inradius and central angle is defined as the line joining the center and one point on circumcircle of pentagon and is represented as rc = (ri)/(cos(Anglecentral/2)) or circumradius = (Inradius)/(cos(Central Angle/2)). Inradius is defined as the radius of the circle which is inscribed inside the polygon & A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.
How to calculate Circumradius of Pentagon given inradius and central angle?
Circumradius of Pentagon given inradius and central angle is defined as the line joining the center and one point on circumcircle of pentagon is calculated using circumradius = (Inradius)/(cos(Central Angle/2)). To calculate Circumradius of Pentagon given inradius and central angle, you need Inradius (ri) & Central Angle (Anglecentral). With our tool, you need to enter the respective value for Inradius & Central Angle 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 & Central Angle. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • circumradius = (Side)/(2*sin(Central Angle/2))
  • circumradius = (Inradius)/(cos(Central Angle/2))
  • circumradius = (0.851*Side)
  • circumradius = (Inradius/0.809)
  • circumradius = Height-Inradius
  • circumradius = (Height)/(1+cos(Central Angle/2))
  • circumradius = (Height/1.809)
  • circumradius = 0.5257*Diagonal
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