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 coincides with the intersection point of the diagonals.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( D_c \) — Diameter of circumcircle (m)
• \( l \) — Length of rectangle (m)
• \( \angle dl \) — Angle between diagonal and length (degrees)
• \( \sec \) — Secant trigonometric function

Explanation: The formula calculates the diameter of the circumcircle using the rectangle's length and the angle between its diagonal and length side.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the circumcircle diameter is important in geometry, engineering design, and architectural planning where circular elements need to encompass rectangular components.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between rectangle dimensions and circumcircle?
A: The diameter of the circumcircle equals the length of the diagonal of the rectangle.

Q2: Can this formula be used for squares?
A: Yes, for squares the angle between diagonal and side is 45°, and the formula simplifies accordingly.

Q3: What is the range of valid angle values?
A: The angle must be between 0° and 90° (exclusive) for meaningful results.

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

Q5: What units should be used for inputs?
A: Length should be in meters, angle in degrees. The calculator handles the conversion to radians internally.