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. It is equal to the length of the diagonal of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( D_c \) — Diameter of circumcircle (m)
• \( l \) — Length of rectangle (m)
• \( \angle_{db} \) — Angle between diagonal and breadth (degrees)
• \( \pi \) — Archimedes' constant (≈ 3.14159)
• \( \sec \) — Secant trigonometric function

Explanation: The formula calculates the diameter of the circumcircle using the length of the rectangle and the angle between the diagonal and the breadth.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the diameter of the circumcircle is important in geometry, engineering, and design applications where circular elements need to encompass rectangular objects or spaces.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the angle between the diagonal and breadth in degrees. The angle must be between 0° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between the circumcircle diameter and the rectangle's diagonal?
A: The diameter of the circumcircle is exactly equal to the length of the rectangle's diagonal.

Q2: Can this formula be used for any rectangle?
A: Yes, this formula applies to all rectangles regardless of their dimensions.

Q3: What is the range of valid angle values?
A: The angle between the diagonal and breadth must be between 0° and 90°.

Q4: How is the secant function calculated?
A: The secant function is the reciprocal of the cosine function: sec(θ) = 1/cos(θ).

Q5: What if I know the breadth instead of the length?
A: You can use a similar formula with the breadth: D_c = b × sec(∠_db), where b is the breadth.