1. What is the 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 a fundamental geometric property that describes the circle passing through all three vertices of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Circumradius - Radius of the circumscribed circle (m)
• Median - Line segment joining a vertex to the midpoint of the opposite side (m)

3. Formula Explanation

Details: In an equilateral triangle, all medians are equal in length and intersect at the centroid. The circumradius is exactly 2/3 the length of any median, as the centroid divides each median in a 2:1 ratio, with the longer segment extending to the circumcenter.

4. Using the Calculator

Tips: Enter the median length of the equilateral triangle in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the circumradius exactly 2/3 of the median?
A: In an equilateral triangle, the centroid, circumcenter, and orthocenter coincide, and the centroid divides each median in a 2:1 ratio, with the longer segment being the circumradius.

Q2: Does this formula work for all types of triangles?
A: No, this specific relationship only holds true for equilateral triangles where all sides and angles are equal.

Q3: What are the units for circumradius?
A: The circumradius has the same units as the input median (typically meters or other length units).

Q4: Can I use this calculator for other triangle types?
A: No, this calculator is specifically designed for equilateral triangles only.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, as it's derived from geometric properties.