Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem 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 2 of Cyclic Quadrilateral is a line segment joining opposite vertices (B and D) of the Cyclic Quadrilateral.ⓘ Diagonal 2 of Cyclic Quadrilateral [d₂]			+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 using Ptolemy's Theorem [d₁]

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Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
d₁ = ((S_a*S_c)+(S_b*S_d))/d₂
This formula uses 6 Variables

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.
Diagonal 2 of Cyclic Quadrilateral - (Measured in Meter) - Diagonal 2 of Cyclic Quadrilateral is a line segment joining opposite vertices (B and D) 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
Diagonal 2 of Cyclic Quadrilateral: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₁ = ((S_a*S_c)+(S_b*S_d))/d₂ --> ((10*8)+(9*5))/12

Evaluating ... ...

d₁ = 10.4166666666667

STEP 3: Convert Result to Output's Unit

10.4166666666667 Meter --> No Conversion Required

FINAL ANSWER

10.4166666666667 ≈ 10.41667 Meter <-- Diagonal 1 of Cyclic Quadrilateral

(Calculation completed in 00.004 seconds)

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< Diagonals of Cyclic Quadrilateral Calculators

Diagonal 1 of Cyclic Quadrilateral

LaTeX 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

LaTeX 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 Theorem

LaTeX 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

LaTeX 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

< 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

LaTeX 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 1 of Cyclic Quadrilateral using Ptolemy's Theorem

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem Formula

LaTeX Go

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 using Ptolemy's Theorem?

Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem calculator uses 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 to calculate the Diagonal 1 of Cyclic Quadrilateral, The Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral, calculated using Ptolemy's Theorem. Diagonal 1 of Cyclic Quadrilateral is denoted by d₁ symbol.

How to calculate Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem using this online calculator? To use this online calculator for Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem, 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) & Diagonal 2 of Cyclic Quadrilateral (d₂) and hit the calculate button. Here is how the Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem calculation can be explained with given input values -> 10.41667 = ((10*8)+(9*5))/12.

FAQ

What is Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem?

The Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral, calculated using Ptolemy's Theorem and is represented as d₁ = ((S_a*S_c)+(S_b*S_d))/d₂ or 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. 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 & Diagonal 2 of Cyclic Quadrilateral is a line segment joining opposite vertices (B and D) of the Cyclic Quadrilateral.

How to calculate Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem?

The Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem formula is defined as the line segment joining opposite vertices (A and C) of the Cyclic Quadrilateral, calculated using Ptolemy's Theorem is calculated using 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. To calculate Diagonal 1 of Cyclic Quadrilateral using Ptolemy's Theorem, 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) & Diagonal 2 of Cyclic Quadrilateral (d₂). 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 & Diagonal 2 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 & Diagonal 2 of Cyclic Quadrilateral. We can use 3 other way(s) to calculate the same, which is/are as follows -

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 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 = 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)))

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