Angle between Diagonals of Cyclic Quadrilateral Calculator

✖Semiperimeter of Cyclic Quadrilateral is half of the sum of all the sides of the Cyclic Quadrilateral.ⓘ Semiperimeter of Cyclic Quadrilateral [s]			+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%
✖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%

✖Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.ⓘ Angle between Diagonals of Cyclic Quadrilateral [∠_Diagonals]

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Formula

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Angle between Diagonals of Cyclic Quadrilateral

Formula

`"∠"_{"Diagonals"} = 2*arctan(sqrt((("s"-"S"_{"b"})*("s"-"S"_{"d"}))/(("s"-"S"_{"a"})*("s"-"S"_{"c"}))))`

Example

`"103.4148°"=2*arctan(sqrt((("16m"-"9m")*("16m"-"5m"))/(("16m"-"10m")*("16m"-"8m"))))`

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Angle between Diagonals of Cyclic Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral))))
∠_Diagonals = 2*arctan(sqrt(((s-S_b)*(s-S_d))/((s-S_a)*(s-S_c))))
This formula uses 4 Functions, 6 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
ctan - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., ctan(Angle)
arctan - Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x)., arctan(Number)
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

Angle Between Diagonals of Cyclic Quadrilateral - (Measured in Radian) - Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.
Semiperimeter of Cyclic Quadrilateral - (Measured in Meter) - Semiperimeter of Cyclic Quadrilateral is half of the sum of all the 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 D of Cyclic Quadrilateral - (Measured in Meter) - Side D of Cyclic Quadrilateral is one of the four sides 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.

STEP 1: Convert Input(s) to Base Unit

Semiperimeter of Cyclic Quadrilateral: 16 Meter --> 16 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
Side A of Cyclic Quadrilateral: 10 Meter --> 10 Meter No Conversion Required
Side C of Cyclic Quadrilateral: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Diagonals = 2*arctan(sqrt(((s-S_b)*(s-S_d))/((s-S_a)*(s-S_c)))) --> 2*arctan(sqrt(((16-9)*(16-5))/((16-10)*(16-8))))

Evaluating ... ...

∠_Diagonals = 1.80492960624819

STEP 3: Convert Result to Output's Unit

1.80492960624819 Radian -->103.41484875625 Degree (Check conversion here)

FINAL ANSWER

103.41484875625 ≈ 103.4148 Degree <-- Angle Between Diagonals of Cyclic Quadrilateral

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Cyclic Quadrilateral » Angle of Cyclic Quadrilateral » Angle between Diagonals of Cyclic Quadrilateral

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< 7 Angle of Cyclic Quadrilateral Calculators

Angle between Diagonals of Cyclic Quadrilateral

Go Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral))))

Angle A of Cyclic Quadrilateral

Go Angle A of Cyclic Quadrilateral = arccos((Side A of Cyclic Quadrilateral^2+Side D of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2-Side C of Cyclic Quadrilateral^2)/(2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))))

Angle D of Cyclic Quadrilateral

Go Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral))))

Angle A of Cyclic Quadrilateral given Angle C

Go Angle A of Cyclic Quadrilateral = pi-Angle C of Cyclic Quadrilateral

Angle D of Cyclic Quadrilateral given Angle B

Go Angle D of Cyclic Quadrilateral = pi-Angle B of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral

Go Angle B of Cyclic Quadrilateral = pi-Angle D of Cyclic Quadrilateral

Angle C of Cyclic Quadrilateral

Go Angle C of Cyclic Quadrilateral = pi-Angle A of Cyclic Quadrilateral

< 5 Angles of Cyclic Quadrilateral Calculators

Angle between Diagonals of Cyclic Quadrilateral

Angle A of Cyclic Quadrilateral

Angle D of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral

Go Angle B of Cyclic Quadrilateral = pi-Angle D of Cyclic Quadrilateral

Angle C of Cyclic Quadrilateral

Go Angle C of Cyclic Quadrilateral = pi-Angle A of Cyclic Quadrilateral

Angle between Diagonals 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 Angle between Diagonals of Cyclic Quadrilateral?

Angle between Diagonals of Cyclic Quadrilateral calculator uses Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)))) to calculate the Angle Between Diagonals of Cyclic Quadrilateral, The Angle between Diagonals of Cyclic Quadrilateral formula is defined as the measure of the angle formed between the diagonals of the Cyclic Quadrilateral. Angle Between Diagonals of Cyclic Quadrilateral is denoted by ∠_Diagonals symbol.

How to calculate Angle between Diagonals of Cyclic Quadrilateral using this online calculator? To use this online calculator for Angle between Diagonals of Cyclic Quadrilateral, enter Semiperimeter of Cyclic Quadrilateral (s), Side B of Cyclic Quadrilateral (S_b), Side D of Cyclic Quadrilateral (S_d), Side A of Cyclic Quadrilateral (S_a) & Side C of Cyclic Quadrilateral (S_c) and hit the calculate button. Here is how the Angle between Diagonals of Cyclic Quadrilateral calculation can be explained with given input values -> 5925.234 = 2*arctan(sqrt(((16-9)*(16-5))/((16-10)*(16-8)))).

FAQ

What is Angle between Diagonals of Cyclic Quadrilateral?

The Angle between Diagonals of Cyclic Quadrilateral formula is defined as the measure of the angle formed between the diagonals of the Cyclic Quadrilateral and is represented as ∠_Diagonals = 2*arctan(sqrt(((s-S_b)*(s-S_d))/((s-S_a)*(s-S_c)))) or Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)))). Semiperimeter of Cyclic Quadrilateral is half of the sum of all the sides of the 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, 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.

How to calculate Angle between Diagonals of Cyclic Quadrilateral?

The Angle between Diagonals of Cyclic Quadrilateral formula is defined as the measure of the angle formed between the diagonals of the Cyclic Quadrilateral is calculated using Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)))). To calculate Angle between Diagonals of Cyclic Quadrilateral, you need Semiperimeter of Cyclic Quadrilateral (s), Side B of Cyclic Quadrilateral (S_b), Side D of Cyclic Quadrilateral (S_d), Side A of Cyclic Quadrilateral (S_a) & Side C of Cyclic Quadrilateral (S_c). With our tool, you need to enter the respective value for Semiperimeter of Cyclic Quadrilateral, Side B of Cyclic Quadrilateral, Side D of Cyclic Quadrilateral, Side A of Cyclic Quadrilateral & Side C of Cyclic Quadrilateral and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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