1. What is Exradius of Equilateral Triangle?

The exradius of an equilateral triangle is the radius of the escribed circle (excircle) that is tangent to one side of the triangle and the extensions of the other two sides. In an equilateral triangle, all three exradii are equal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula establishes the relationship between the exradius and circumradius of an equilateral triangle, showing that the exradius is exactly 1.5 times the circumradius.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry for determining the size of the excircle, which has applications in various geometric constructions and proofs involving equilateral triangles.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between circumradius and exradius?
A: The circumradius is the radius of the circle that passes through all three vertices of the triangle, while the exradius is the radius of the circle tangent to one side and the extensions of the other two sides.

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

Q4: What are practical applications of exradius calculation?
A: Exradius calculations are used in geometric design, architecture, and various engineering applications where precise circle-triangle relationships are needed.

Q5: How is the exradius related to the side length of an equilateral triangle?
A: The exradius can also be expressed as \( r_e = \frac{\sqrt{3}}{2} \times a \), where a is the side length of the equilateral triangle.