Circumradius of Cyclic Quadrilateral given Area Calculator

✖Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side A of Cyclic Quadrilateral [S_a]			+10% -10%
✖Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side B of Cyclic Quadrilateral [S_b]			+10% -10%
✖Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.ⓘ Side C of Cyclic Quadrilateral [S_c]			+10% -10%
✖Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side D of Cyclic Quadrilateral [S_d]			+10% -10%
✖Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.ⓘ Area of Cyclic Quadrilateral [A]			+10% -10%

✖Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.ⓘ Circumradius of Cyclic Quadrilateral given Area [r_c]

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Formula

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Circumradius of Cyclic Quadrilateral given Area

Formula

`"r"_{"c"} = sqrt((("S"_{"a"}*"S"_{"b"})+("S"_{"c"}*"S"_{"d"}))*(("S"_{"a"}*"S"_{"c"})+("S"_{"b"}*"S"_{"d"}))*(("S"_{"a"}*"S"_{"d"})+("S"_{"c"}*"S"_{"b"})))/(4*"A")`

Example

`"5.86672m"=sqrt((("10m"*"9m")+("8m"*"5m"))*(("10m"*"8m")+("9m"*"5m"))*(("10m"*"5m")+("8m"*"9m")))/(4*"60m²")`

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Circumradius of Cyclic Quadrilateral given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Area of Cyclic Quadrilateral)
r_c = sqrt(((S_a*S_b)+(S_c*S_d))*((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_c*S_b)))/(4*A)
This formula uses 1 Functions, 6 Variables

Functions Used

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., sqrt(Number)

Variables Used

Circumradius of Cyclic Quadrilateral - (Measured in Meter) - Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.
Side A of Cyclic Quadrilateral - (Measured in Meter) - Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.
Side B of Cyclic Quadrilateral - (Measured in Meter) - Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.
Side C of Cyclic Quadrilateral - (Measured in Meter) - Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.
Side D of Cyclic Quadrilateral - (Measured in Meter) - Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.
Area of Cyclic Quadrilateral - (Measured in Square Meter) - Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

Side A of Cyclic Quadrilateral: 10 Meter --> 10 Meter No Conversion Required
Side B of Cyclic Quadrilateral: 9 Meter --> 9 Meter No Conversion Required
Side C of Cyclic Quadrilateral: 8 Meter --> 8 Meter No Conversion Required
Side D of Cyclic Quadrilateral: 5 Meter --> 5 Meter No Conversion Required
Area of Cyclic Quadrilateral: 60 Square Meter --> 60 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(((S_a*S_b)+(S_c*S_d))*((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_c*S_b)))/(4*A) --> sqrt(((10*9)+(8*5))*((10*8)+(9*5))*((10*5)+(8*9)))/(4*60)

Evaluating ... ...

r_c = 5.8667199334703

STEP 3: Convert Result to Output's Unit

5.8667199334703 Meter --> No Conversion Required

FINAL ANSWER

5.8667199334703 ≈ 5.86672 Meter <-- Circumradius of Cyclic Quadrilateral

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Cyclic Quadrilateral » Radius of Cyclic Quadrilateral » Circumradius of Cyclic Quadrilateral given Area

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< 3 Radius of Cyclic Quadrilateral Calculators

Circumradius of Cyclic Quadrilateral

Go Circumradius of Cyclic Quadrilateral = 1/4*(sqrt((((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))))

Circumradius of Cyclic Quadrilateral given Perimeter

Go Circumradius of Cyclic Quadrilateral = 1/4*(sqrt((((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))/((Perimeter of Cyclic Quadrilateral/2-Side A of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side B of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side C of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side D of Cyclic Quadrilateral))))

Circumradius of Cyclic Quadrilateral given Area

Go Circumradius of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Area of Cyclic Quadrilateral)

< 4 Other Formulas of Cyclic Quadrilateral Calculators

Circumradius of Cyclic Quadrilateral

Circumradius of Cyclic Quadrilateral given Area

Perimeter of Cyclic Quadrilateral

Go Perimeter of Cyclic Quadrilateral = Side A of Cyclic Quadrilateral+Side B of Cyclic Quadrilateral+Side C of Cyclic Quadrilateral+Side D of Cyclic Quadrilateral

Semiperimeter of Cyclic Quadrilateral

Go Semiperimeter of Cyclic Quadrilateral = Perimeter of Cyclic Quadrilateral/2

Circumradius of Cyclic Quadrilateral given Area Formula

What is a Cyclic Quadrilateral?

A Cyclic Quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that there exists a circle that passes through all four vertices of the quadrilateral. Cyclic quadrilaterals are useful in various types of geometry problems, particularly those in which angle chasing is required.

How to Calculate Circumradius of Cyclic Quadrilateral given Area?

Circumradius of Cyclic Quadrilateral given Area calculator uses Circumradius of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Area of Cyclic Quadrilateral) to calculate the Circumradius of Cyclic Quadrilateral, The Circumradius of Cyclic Quadrilateral given Area formula is defined as the distance between the circumcentre and any one of the vertices of the Cyclic Quadrilateral, calculated using its area. Circumradius of Cyclic Quadrilateral is denoted by r_c symbol.

How to calculate Circumradius of Cyclic Quadrilateral given Area using this online calculator? To use this online calculator for Circumradius of Cyclic Quadrilateral given Area, enter Side A of Cyclic Quadrilateral (S_a), Side B of Cyclic Quadrilateral (S_b), Side C of Cyclic Quadrilateral (S_c), Side D of Cyclic Quadrilateral (S_d) & Area of Cyclic Quadrilateral (A) and hit the calculate button. Here is how the Circumradius of Cyclic Quadrilateral given Area calculation can be explained with given input values -> 5.86672 = sqrt(((10*9)+(8*5))*((10*8)+(9*5))*((10*5)+(8*9)))/(4*60).

FAQ

What is Circumradius of Cyclic Quadrilateral given Area?

The Circumradius of Cyclic Quadrilateral given Area formula is defined as the distance between the circumcentre and any one of the vertices of the Cyclic Quadrilateral, calculated using its area and is represented as r_c = sqrt(((S_a*S_b)+(S_c*S_d))*((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_c*S_b)))/(4*A) or Circumradius of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Area of Cyclic Quadrilateral). Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral, Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral, Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral, Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral & Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.

How to calculate Circumradius of Cyclic Quadrilateral given Area?

The Circumradius of Cyclic Quadrilateral given Area formula is defined as the distance between the circumcentre and any one of the vertices of the Cyclic Quadrilateral, calculated using its area is calculated using Circumradius of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Area of Cyclic Quadrilateral). To calculate Circumradius of Cyclic Quadrilateral given Area, you need Side A of Cyclic Quadrilateral (S_a), Side B of Cyclic Quadrilateral (S_b), Side C of Cyclic Quadrilateral (S_c), Side D of Cyclic Quadrilateral (S_d) & Area of Cyclic Quadrilateral (A). With our tool, you need to enter the respective value for Side A of Cyclic Quadrilateral, Side B of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side D of Cyclic Quadrilateral & Area of Cyclic Quadrilateral 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 Cyclic Quadrilateral?

In this formula, Circumradius of Cyclic Quadrilateral uses Side A of Cyclic Quadrilateral, Side B of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side D of Cyclic Quadrilateral & Area of Cyclic Quadrilateral. We can use 3 other way(s) to calculate the same, which is/are as follows -

Circumradius of Cyclic Quadrilateral = 1/4*(sqrt((((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))))
Circumradius of Cyclic Quadrilateral = 1/4*(sqrt((((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))/((Perimeter of Cyclic Quadrilateral/2-Side A of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side B of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side C of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side D of Cyclic Quadrilateral))))
Circumradius of Cyclic Quadrilateral = 1/4*(sqrt((((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))))

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