1. What is the Inradius of Equilateral Triangle?

The Inradius of an Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle. It is the distance from the center of the inscribed circle (incircle) to any side of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Equilateral Triangle (m)
• \( l_{\text{Angle Bisector}} \) — Length of Angle Bisector of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the inradius is exactly one-third the length of the angle bisector, as all three angle bisectors are equal and intersect at the incenter.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside an equilateral triangle, which has applications in various engineering and design fields.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the inradius exactly one-third of the angle bisector length?
A: In an equilateral triangle, the angle bisector, median, and altitude are all the same line. The incenter divides these lines in a 2:1 ratio, making the inradius one-third of the total length.

Q2: Can this formula be used for other 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 of measurement for the inradius?
A: The inradius will have the same units as the input length of the angle bisector (typically meters).

Q4: How is the angle bisector length related to the side length?
A: In an equilateral triangle with side length 'a', the angle bisector length is \( \frac{\sqrt{3}}{2} \times a \).

Q5: What is the relationship between inradius and circumradius?
A: In an equilateral triangle, the circumradius is exactly twice the inradius.