1. What is Exradius of Equilateral Triangle?

The Exradius of an Equilateral Triangle is the radius of the escribed circle (excircle) of the triangle. In an equilateral triangle, all exradii are equal and can be calculated from the median length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Median - The median length of the equilateral triangle

Explanation: In an equilateral triangle, the exradius is equal to the median length since all medians, altitudes, and angle bisectors coincide and have the same length.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry for determining the size of the excircle, which is tangent to one side of the triangle and the extensions of the other two sides.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between exradius and median in an equilateral triangle?
A: In an equilateral triangle, the exradius is equal to the median length.

Q2: Are all exradii equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all three exradii are equal due to the symmetry of the triangle.

Q3: How is exradius different from inradius?
A: The exradius is the radius of an excircle (outside the triangle), while the inradius is the radius of the incircle (inside the triangle).

Q4: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles. Other triangle types have different relationships between exradius and median.

Q5: What are the practical applications of exradius calculation?
A: Exradius calculations are used in various geometric constructions, architectural designs, and engineering applications involving triangular shapes.