1. What is Circumradius of Equilateral Triangle?

The Circumradius of Equilateral Triangle is the radius of a circumcircle touching each of the Equilateral Triangle's vertices. It's an important geometric property that helps in various geometric calculations and constructions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Equilateral Triangle (m)
• \( r_e \) — Exradius of Equilateral Triangle (m)

Explanation: This formula establishes the relationship between the circumradius and exradius of an equilateral triangle, where the circumradius is exactly two-thirds of the exradius.

3. Importance of Circumradius Calculation

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

4. Using the Calculator

Tips: Enter the exradius value in meters. The value must be positive and greater than zero to get accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and exradius?
A: In an equilateral triangle, the circumradius is exactly two-thirds of the exradius.

Q2: Can this formula be used for other types of triangles?
A: No, this specific relationship only applies to equilateral triangles where all sides and angles are equal.

Q3: What are the units for circumradius and exradius?
A: Both are measured in meters or any consistent length unit.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles.

Q5: What is the practical application of knowing the circumradius?
A: It's used in various geometric constructions, CAD designs, and in calculating properties of circumscribed circles.