Diameter Of Circumcircle Of Rectangle Given Breadth And Obtuse Angle Between Diagonals Calculator

Formula Used:

\[ D_c = b \times \csc\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right) \]

Diameter of Circumcircle of Rectangle:

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1. What is the Diameter of Circumcircle of Rectangle?

The diameter of the circumcircle of a rectangle is the diameter of the circle that passes through all four vertices of the rectangle. For any rectangle, the circumcircle's center is at the intersection of the diagonals, and its diameter equals the length of the diagonal of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_c = b \times \csc\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right) \]

Where:

\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( b \) — Breadth of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals of Rectangle (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \csc \) — Cosecant trigonometric function

Explanation: This formula calculates the diameter of the circumcircle using the breadth of the rectangle and the obtuse angle between its diagonals, leveraging trigonometric relationships in rectangular geometry.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the circumcircle diameter is important in various geometric and engineering applications, particularly in design and construction where circular elements interact with rectangular components.

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the obtuse angle between diagonals in degrees. The angle must be between 90° and 180° (exclusive), and the breadth must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle between diagonals important?
A: The angle between diagonals helps determine the shape's proportions and is crucial for calculating various geometric properties, including the circumcircle diameter.

Q2: What is the relationship between the diagonal and circumcircle diameter?
A: For a rectangle, the circumcircle diameter is exactly equal to the length of the diagonal of the rectangle.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula applies to squares as well.

Q4: What if I know the length instead of the breadth?
A: The formula can be adapted using trigonometric relationships, but this specific calculator requires the breadth as input.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and proper implementation of trigonometric functions.