1. What is Circumradius of Cyclic Quadrilateral?

The circumradius of a cyclic quadrilateral is the radius of the circumscribed circle that passes through all four vertices of the quadrilateral. A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

Where:

• \( R \) — Circumradius
• \( a, b, c, d \) — Sides of the cyclic quadrilateral
• \( s \) — Semiperimeter = \( \frac{a + b + c + d}{2} \)

Explanation: This formula calculates the radius of the circle that circumscribes a cyclic quadrilateral based on its side lengths.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, engineering, and architecture for designing circular structures and understanding the geometric properties of cyclic quadrilaterals.

4. Using the Calculator

Tips: Enter all four side lengths in meters. All values must be positive numbers. The quadrilateral must be cyclic (able to be inscribed in a circle).

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle. The circle is called the circumcircle.

Q2: Can any quadrilateral be cyclic?
A: No, only quadrilaterals where opposite angles sum to 180° can be cyclic (Ptolemy's theorem).

Q3: What are some examples of cyclic quadrilaterals?
A: Squares, rectangles, and isosceles trapezoids are all cyclic quadrilaterals.

Q4: What if I get an error message?
A: The error indicates the side lengths cannot form a cyclic quadrilateral. Check your measurements and ensure the quadrilateral satisfies the condition for being cyclic.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for any valid cyclic quadrilateral, though practical accuracy depends on the precision of your input measurements.