Diagonal 1 of Cyclic Quadrilateral 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 C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.ⓘ Side C of Cyclic Quadrilateral [S_c]			+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 D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side D of Cyclic Quadrilateral [S_d]			+10% -10%

✖Diagonal 1 of Cyclic Quadrilateral is a line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral.ⓘ Diagonal 1 of Cyclic Quadrilateral [d₁]

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Formula

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Diagonal 1 of Cyclic Quadrilateral

Formula

`"d"_{"1"} = sqrt(((("S"_{"a"}*"S"_{"c"})+("S"_{"b"}*"S"_{"d"}))*(("S"_{"a"}*"S"_{"d"})+("S"_{"b"}*"S"_{"c"})))/(("S"_{"a"}*"S"_{"b"})+("S"_{"c"}*"S"_{"d"})))`

Example

`"10.83087m"=sqrt(((("10m"*"8m")+("9m"*"5m"))*(("10m"*"5m")+("9m"*"8m")))/(("10m"*"9m")+("8m"*"5m")))`

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Diagonal 1 of Cyclic Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal 1 of Cyclic Quadrilateral = sqrt((((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)))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)))
d₁ = sqrt((((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_b*S_c)))/((S_a*S_b)+(S_c*S_d)))
This formula uses 1 Functions, 5 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

Diagonal 1 of Cyclic Quadrilateral - (Measured in Meter) - Diagonal 1 of Cyclic Quadrilateral is a line segment joining opposite vertices (A and C) 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 C of Cyclic Quadrilateral - (Measured in Meter) - Side C of Cyclic Quadrilateral is one of the four sides of 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 D of Cyclic Quadrilateral - (Measured in Meter) - Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₁ = sqrt((((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_b*S_c)))/((S_a*S_b)+(S_c*S_d))) --> sqrt((((10*8)+(9*5))*((10*5)+(9*8)))/((10*9)+(8*5)))

Evaluating ... ...

d₁ = 10.8308675694836

STEP 3: Convert Result to Output's Unit

10.8308675694836 Meter --> No Conversion Required

FINAL ANSWER

10.8308675694836 ≈ 10.83087 Meter <-- Diagonal 1 of Cyclic Quadrilateral

(Calculation completed in 00.004 seconds)

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< 6 Diagonals of Cyclic Quadrilateral Calculators

Diagonal 1 of Cyclic Quadrilateral

Go Diagonal 1 of Cyclic Quadrilateral = sqrt((((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)))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)))

Diagonal 2 of Cyclic Quadrilateral

Go Diagonal 2 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)))

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Second Theorem

Go Diagonal 1 of Cyclic Quadrilateral = (((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)))*Diagonal 2 of Cyclic Quadrilateral

Diagonal 2 of Cyclic Quadrilateral using Ptolemy's Second Theorem

Go Diagonal 2 of Cyclic Quadrilateral = (((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 D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))*Diagonal 1 of Cyclic Quadrilateral

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem

Go Diagonal 1 of Cyclic Quadrilateral = ((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))/Diagonal 2 of Cyclic Quadrilateral

Diagonal 2 of Cyclic Quadrilateral using Ptolemy's Theorem

Go Diagonal 2 of Cyclic Quadrilateral = ((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))/Diagonal 1 of Cyclic Quadrilateral

< 4 Diagonals of Cyclic Quadrilateral Calculators

Diagonal 1 of Cyclic Quadrilateral

Diagonal 2 of Cyclic Quadrilateral

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Second Theorem

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem

Diagonal 1 of Cyclic Quadrilateral 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 Diagonal 1 of Cyclic Quadrilateral?

Diagonal 1 of Cyclic Quadrilateral calculator uses Diagonal 1 of Cyclic Quadrilateral = sqrt((((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)))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))) to calculate the Diagonal 1 of Cyclic Quadrilateral, The Diagonal 1 of Cyclic Quadrilateral formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral. Diagonal 1 of Cyclic Quadrilateral is denoted by d₁ symbol.

How to calculate Diagonal 1 of Cyclic Quadrilateral using this online calculator? To use this online calculator for Diagonal 1 of Cyclic Quadrilateral, enter Side A of Cyclic Quadrilateral (S_a), Side C of Cyclic Quadrilateral (S_c), Side B of Cyclic Quadrilateral (S_b) & Side D of Cyclic Quadrilateral (S_d) and hit the calculate button. Here is how the Diagonal 1 of Cyclic Quadrilateral calculation can be explained with given input values -> 10.83087 = sqrt((((10*8)+(9*5))*((10*5)+(9*8)))/((10*9)+(8*5))).

FAQ

What is Diagonal 1 of Cyclic Quadrilateral?

The Diagonal 1 of Cyclic Quadrilateral formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral and is represented as d₁ = sqrt((((S_a*S_c)+(S_b*S_d))*((S_a*S_d)+(S_b*S_c)))/((S_a*S_b)+(S_c*S_d))) or Diagonal 1 of Cyclic Quadrilateral = sqrt((((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)))/((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 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 B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral & Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

How to calculate Diagonal 1 of Cyclic Quadrilateral?

The Diagonal 1 of Cyclic Quadrilateral formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral is calculated using Diagonal 1 of Cyclic Quadrilateral = sqrt((((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)))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))). To calculate Diagonal 1 of Cyclic Quadrilateral, you need Side A of Cyclic Quadrilateral (S_a), Side C of Cyclic Quadrilateral (S_c), Side B of Cyclic Quadrilateral (S_b) & Side D of Cyclic Quadrilateral (S_d). With our tool, you need to enter the respective value for Side A of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side B of Cyclic Quadrilateral & Side D 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 Diagonal 1 of Cyclic Quadrilateral?

In this formula, Diagonal 1 of Cyclic Quadrilateral uses Side A of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side B of Cyclic Quadrilateral & Side D of Cyclic Quadrilateral. We can use 4 other way(s) to calculate the same, which is/are as follows -

Diagonal 1 of Cyclic Quadrilateral = ((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))/Diagonal 2 of Cyclic Quadrilateral
Diagonal 1 of Cyclic Quadrilateral = (((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)))*Diagonal 2 of Cyclic Quadrilateral
Diagonal 1 of Cyclic Quadrilateral = (((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))/((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)))*Diagonal 2 of Cyclic Quadrilateral
Diagonal 1 of Cyclic Quadrilateral = ((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))/Diagonal 2 of Cyclic Quadrilateral

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