1. What is the Circumradius of Equilateral Triangle?

The Circumradius of an Equilateral Triangle is the radius of the circumscribed circle that passes through all three vertices of the triangle. It is a fundamental geometric property that relates to various other measurements of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Equilateral Triangle (m)
• \( l_{\text{Angle Bisector}} \) — Length of Angle Bisector of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the circumradius is directly proportional to the length of the angle bisector, with a constant ratio of 2/3.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry for determining the size of the circumscribed circle, which has applications in various fields including engineering, architecture, and computer graphics.

4. Using the Calculator

Tips: Enter the length of the angle bisector in meters. The value must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and side length?
A: In an equilateral triangle, circumradius = side length / √3.

Q2: How does circumradius relate to inradius?
A: In an equilateral triangle, circumradius = 2 × inradius.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.

Q4: What are practical applications of circumradius calculation?
A: Used in designing circular structures, mechanical parts, and in computational geometry algorithms.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, providing precise results.