1. What is Exradius of Equilateral Triangle?

The Exradius of an Equilateral Triangle is the radius of the escribed circle (excircle) of the triangle. An excircle is a circle tangent to one side of the triangle and the extensions of the other two sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_e \) — Exradius of Equilateral Triangle (m)
• \( l_{Angle\ Bisector} \) — Length of Angle Bisector of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the exradius is equal to the length of the angle bisector, as all angle bisectors, medians, and altitudes coincide and have equal lengths.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry for determining properties of triangles, constructing excircles, and solving various geometric problems involving equilateral triangles.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: Are all angle bisectors equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all angle bisectors, medians, and altitudes are equal in length.

Q3: How is the exradius related to other triangle elements?
A: The exradius can also be related to the side length and other geometric properties of the triangle.

Q4: Can this calculator be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.

Q5: What are practical applications of calculating exradius?
A: Exradius calculations are used in various fields including architecture, engineering, and computer graphics where geometric properties of triangles are important.