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

Formula Used:

\[ D_c = \frac{l}{\cos\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)} \]

Diameter of Circumcircle:

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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 point 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:

\[ D_c = \frac{l}{\cos\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)} \]

Where:

\( D_c \) — Diameter of circumcircle (m)
\( l \) — Length of rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse angle between diagonals (radians)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula derives from the geometric relationship between the rectangle's dimensions, its diagonals, and the circumcircle that passes through its vertices.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the circumcircle diameter is important in various geometric applications, construction projects, and engineering designs where circular elements need to encompass rectangular components.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the obtuse angle between diagonals in degrees (must be between 90° and 180°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle between diagonals important?
A: The angle between diagonals determines the shape of the rectangle and directly affects the circumcircle diameter calculation.

Q2: What is the relationship between rectangle dimensions and circumcircle?
A: For any rectangle, the circumcircle's diameter equals the length of the diagonal, which can be calculated using the Pythagorean theorem.

Q3: Can this formula be used for squares?
A: Yes, for squares (where length equals width), the angle between diagonals is 90°, and the formula simplifies accordingly.

Q4: What are practical applications of this calculation?
A: This calculation is useful in architecture, mechanical engineering, and graphic design when working with rectangular elements within circular boundaries.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect rectangles, with accuracy depending on the precision of input values.