Circumradius of Pentagon given Inradius using Interior Angle Calculator

✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon [r_i]

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✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon given Inradius using Interior Angle [r_c]

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Circumradius of Pentagon given Inradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi))
r_c = r_i/(1/2-cos(3/5*pi))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = r_i/(1/2-cos(3/5*pi)) --> 7/(1/2-cos(3/5*pi))

Evaluating ... ...

r_c = 8.65247584249853

STEP 3: Convert Result to Output's Unit

8.65247584249853 Meter --> No Conversion Required

FINAL ANSWER

8.65247584249853 ≈ 8.652476 Meter <-- Circumradius of Pentagon

(Calculation completed in 00.004 seconds)

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< Circumradius of Pentagon Calculators

Circumradius of Pentagon given Inradius

LaTeX Go Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))

Circumradius of Pentagon

LaTeX Go Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))

Circumradius of Pentagon given Edge Length using Central Angle

LaTeX Go Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))

Circumradius of Pentagon given Inradius using Central Angle

LaTeX Go Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))

Circumradius of Pentagon given Inradius using Interior Angle Formula

LaTeX Go

Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi))
r_c = r_i/(1/2-cos(3/5*pi))

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

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

Circumradius of Pentagon given Inradius using Interior Angle calculator uses Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)) to calculate 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 calculate Circumradius of Pentagon given Inradius using Interior Angle using this online calculator? To use this online calculator for Circumradius of Pentagon given Inradius using Interior Angle, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Circumradius of Pentagon given Inradius using Interior Angle calculation can be explained with given input values -> 8.652476 = 7/(1/2-cos(3/5*pi)).

FAQ

What is Circumradius of Pentagon given Inradius using Interior Angle?

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 and is represented as r_c = r_i/(1/2-cos(3/5*pi)) or Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)). The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

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

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 is calculated using Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi)). To calculate Circumradius of Pentagon given Inradius using Interior Angle, you need Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for Inradius of Pentagon 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 Pentagon?

In this formula, Circumradius of Pentagon uses Inradius of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)))

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