1. What is Circumradius of Rectangle?

The circumradius of a rectangle is the radius of the circle that passes through all four vertices of the rectangle. Since all rectangles are cyclic quadrilaterals, they can be inscribed in a circle, and the circumradius is half the length of the diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Rectangle (m)
• \( l \) — Length of Rectangle (m)
• \( \angle db \) — Angle between Diagonal and Breadth of Rectangle (rad)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sec \) — Secant trigonometric function

Explanation: This formula calculates the circumradius based on the length of the rectangle and the angle between its diagonal and breadth, using trigonometric relationships.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, engineering, and design applications where circular patterns or circumscribed circles around rectangular objects are involved.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the angle between the diagonal and breadth in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and diagonal?
A: The circumradius of a rectangle is exactly half the length of its diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, this formula applies to squares as well.

Q3: What is the range of valid angle values?
A: The angle between diagonal and breadth should be between 0 and π/2 radians (0-90 degrees).

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 are practical applications of circumradius calculation?
A: This calculation is used in mechanical engineering, architecture, computer graphics, and various design fields where circular patterns around rectangular objects are needed.