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Circumradius of Cyclic Quadrilateral given Area Formula

GoCircumradius of Cyclic Quadrilateral Formula

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Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral. Check FAQs

r c = \frac{\sqrt{((S a \cdot S b) + (S c \cdot S d)) \cdot ((S a \cdot S c) + (S b \cdot S d)) \cdot ((S a \cdot S d) + (S c \cdot S b))}}{4 \cdot A}

r_c - Circumradius of Cyclic Quadrilateral?S_a - Side A of Cyclic Quadrilateral?S_b - Side B of Cyclic Quadrilateral?S_c - Side C of Cyclic Quadrilateral?S_d - Side D of Cyclic Quadrilateral?A - Area of Cyclic Quadrilateral?

Circumradius of Cyclic Quadrilateral given Area Example

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Here is how the Circumradius of Cyclic Quadrilateral given Area equation looks like with Values.

Here is how the Circumradius of Cyclic Quadrilateral given Area equation looks like with Units.

Here is how the Circumradius of Cyclic Quadrilateral given Area equation looks like.

5.8667 = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 60}

5.8667m = \frac{\sqrt{((10m \cdot 9m) + (8m \cdot 5m)) \cdot ((10m \cdot 8m) + (9m \cdot 5m)) \cdot ((10m \cdot 5m) + (8m \cdot 9m))}}{4 \cdot 60m²}

5.8667 = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 60}

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Circumradius of Cyclic Quadrilateral given Area Solution

Follow our step by step solution on how to calculate Circumradius of Cyclic Quadrilateral given Area?

FIRST Step Consider the formula

r c = \frac{\sqrt{((S a \cdot S b) + (S c \cdot S d)) \cdot ((S a \cdot S c) + (S b \cdot S d)) \cdot ((S a \cdot S d) + (S c \cdot S b))}}{4 \cdot A}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{((10m \cdot 9m) + (8m \cdot 5m)) \cdot ((10m \cdot 8m) + (9m \cdot 5m)) \cdot ((10m \cdot 5m) + (8m \cdot 9m))}}{4 \cdot 60m²}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 60}

Next Step Evaluate

∴

r c = 5.8667199334703m

LAST Step Rounding Answer

∴

r c = 5.8667m

Circumradius of Cyclic Quadrilateral given Area Formula Elements

Variables

Functions

Circumradius of Cyclic Quadrilateral

Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Cyclic Quadrilateral

Side A of Cyclic Quadrilateral

Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side D of Cyclic Quadrilateral

Area of Cyclic Quadrilateral

Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Cyclic Quadrilateral

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.

Syntax: sqrt(Number)

Other Formulas to find Circumradius of Cyclic Quadrilateral

Go Circumradius of Cyclic Quadrilateral

r c = \frac{1}{4} \cdot (\sqrt{\frac{((S a \cdot S b) + (S c \cdot S d)) \cdot ((S a \cdot S c) + (S b \cdot S d)) \cdot ((S a \cdot S d) + (S b \cdot S c))}{(s - S a) \cdot (s - S b) \cdot (s - S c) \cdot (s - S d)}})

Other formulas in Radius of Cyclic Quadrilateral category

Go Perimeter of Cyclic Quadrilateral

P = S a + S b + S c + S d

Go Semiperimeter of Cyclic Quadrilateral

s = \frac{P}{2}

How to Evaluate Circumradius of Cyclic Quadrilateral given Area?

Circumradius of Cyclic Quadrilateral given Area evaluator 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 evaluate 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 evaluate Circumradius of Cyclic Quadrilateral given Area using this online evaluator? To use this online evaluator 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.

FAQs on Circumradius of Cyclic Quadrilateral given Area

What is the formula to find Circumradius of Cyclic Quadrilateral given Area?

The formula of Circumradius of Cyclic Quadrilateral given Area is expressed as 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). Here is an example- 5.86672 = sqrt(((10*9)+(8*5))*((10*8)+(9*5))*((10*5)+(8*9)))/(4*60).

How to calculate Circumradius of Cyclic Quadrilateral given Area?

With 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) we can find Circumradius of Cyclic Quadrilateral given Area using the formula - 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). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Cyclic Quadrilateral?

Here are the different ways to Calculate Circumradius 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))))

Can the Circumradius of Cyclic Quadrilateral given Area be negative?

No, the Circumradius of Cyclic Quadrilateral given Area, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Cyclic Quadrilateral given Area?

Circumradius of Cyclic Quadrilateral given Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Cyclic Quadrilateral given Area can be measured.

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Circumradius of Cyclic Quadrilateral given Area Formula

​GoCircumradius of Cyclic Quadrilateral Formula

Circumradius of Cyclic Quadrilateral given Area Example

Circumradius of Cyclic Quadrilateral given Area Solution

Circumradius of Cyclic Quadrilateral given Area Formula Elements

Other Formulas to find Circumradius of Cyclic Quadrilateral

Other formulas in Radius of Cyclic Quadrilateral category

How to Evaluate Circumradius of Cyclic Quadrilateral given Area?

FAQs on Circumradius of Cyclic Quadrilateral given Area

Variable Name

GoCircumradius of Cyclic Quadrilateral Formula