Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Calculator

✖Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.ⓘ Perimeter of Rectangle [P]			+10% -10%
✖Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.ⓘ Obtuse Angle between Diagonals of Rectangle [∠_d(Obtuse)]			+10% -10%

✖Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.ⓘ Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals [D_c]

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Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))
D_c = P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2))))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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

Diameter of Circumcircle of Rectangle - (Measured in Meter) - Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.
Perimeter of Rectangle - (Measured in Meter) - Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Obtuse Angle between Diagonals of Rectangle - (Measured in Radian) - Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Rectangle: 28 Meter --> 28 Meter No Conversion Required
Obtuse Angle between Diagonals of Rectangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_c = P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2)))) --> 28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2))))

Evaluating ... ...

D_c = 10.0522106028634

STEP 3: Convert Result to Output's Unit

10.0522106028634 Meter --> No Conversion Required

FINAL ANSWER

10.0522106028634 ≈ 10.05221 Meter <-- Diameter of Circumcircle of Rectangle

(Calculation completed in 00.004 seconds)

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< Circumcircle of Rectangle Calculators

Diameter of Circumcircle of Rectangle given Area and Breadth

LaTeX Go Diameter of Circumcircle of Rectangle = sqrt((Area of Rectangle/Breadth of Rectangle)^2+Breadth of Rectangle^2)

Diameter of Circumcircle of Rectangle given Area and Length

LaTeX Go Diameter of Circumcircle of Rectangle = sqrt((Area of Rectangle/Length of Rectangle)^2+Length of Rectangle^2)

Diameter of Circumcircle of Rectangle

LaTeX Go Diameter of Circumcircle of Rectangle = sqrt(Length of Rectangle^2+Breadth of Rectangle^2)

Diameter of Circumcircle of Rectangle given Circumradius

LaTeX Go Diameter of Circumcircle of Rectangle = 2*Circumradius of Rectangle

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

LaTeX Go

Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))
D_c = P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2))))

What is a Rectangle?

A Rectangle is a two dimensional geometric shape having four sides and four corners. The four sides are in two pairs, in which each pair of lines are equal in length and parallel to each other. And adjacent sides are perpendicular to each other. In general a 2D shape with four boundary edges are called quadrilaterals. So a rectangle is a quadrilateral in which each corner is right angle.

How to Calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals calculator uses Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))) to calculate the Diameter of Circumcircle of Rectangle, The Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and obtuse angle between diagonals of the Rectangle. Diameter of Circumcircle of Rectangle is denoted by D_c symbol.

How to calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online calculator? To use this online calculator for Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals, enter Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) and hit the calculate button. Here is how the Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals calculation can be explained with given input values -> 10.05221 = 28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2)))).

FAQ

What is Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

The Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and obtuse angle between diagonals of the Rectangle and is represented as D_c = P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2)))) or Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle & Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

How to calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

The Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and obtuse angle between diagonals of the Rectangle is calculated using Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). To calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals, you need Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)). With our tool, you need to enter the respective value for Perimeter of Rectangle & Obtuse Angle between Diagonals of Rectangle 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 Diameter of Circumcircle of Rectangle?

In this formula, Diameter of Circumcircle of Rectangle uses Perimeter of Rectangle & Obtuse Angle between Diagonals of Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Diameter of Circumcircle of Rectangle = sqrt(Length of Rectangle^2+Breadth of Rectangle^2)
Diameter of Circumcircle of Rectangle = 2*Circumradius of Rectangle
Diameter of Circumcircle of Rectangle = sqrt((Area of Rectangle/Length of Rectangle)^2+Length of Rectangle^2)

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