1. What is Circumradius of Rectangle?

The circumradius of a rectangle is the radius of the circle which contains the rectangle with all the vertices of the rectangle lying on the circle. For any rectangle, the circumradius is equal to half the length of the diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Rectangle (m)
• \( b \) — Breadth of Rectangle (m)
• \( \angle d_{Acute} \) — Acute Angle between Diagonals of Rectangle (°)
• \( \cosec \) — Cosecant trigonometric function

Explanation: The formula calculates the circumradius using the breadth of the rectangle and half of the acute angle between its diagonals through trigonometric relationships.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry and various engineering applications where circular containment or circumscription of rectangular shapes is involved.

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the acute angle between diagonals in degrees. Both values must be positive, with the angle between 0 and 90 degrees.

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 possible circumradius values?
A: The circumradius can be any positive value, depending on the size of the rectangle.

Q4: How is the acute angle between diagonals measured?
A: The acute angle is the smaller angle formed where the two diagonals intersect, always between 0 and 90 degrees.

Q5: What are practical applications of circumradius calculation?
A: This calculation is used in various fields including architecture, mechanical engineering, and computer graphics for circular bounding and containment problems.