1. What is the Inradius of a Triangle?

The inradius of a triangle is the radius of the largest circle that fits inside the triangle and is tangent to all three sides. It represents the distance from the incenter (center of the inscribed circle) to any side of the triangle.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of the triangle
• \( S_a \) — Length of side A of the triangle
• \( S_b \) — Length of side B of the triangle
• \( S_c \) — Length of side C of the triangle

Explanation: This formula calculates the inradius using Heron's formula for area and the relationship between area, semi-perimeter, and inradius.

3. Importance of Inradius Calculation

Details: The inradius is important in geometry for calculating the area of the inscribed circle, understanding triangle properties, and solving various geometric problems involving triangles and circles.

4. Using the Calculator

Tips: Enter the lengths of all three sides of the triangle in meters. All values must be positive numbers, and the sides must satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the side lengths?
A: You can use any consistent units (meters, centimeters, inches, etc.). The inradius will be in the same units as the input sides.

Q2: What if the sides don't form a valid triangle?
A: The calculator will display an error message if the input sides violate the triangle inequality theorem (sum of any two sides must be greater than the third side).

Q3: How is inradius related to area?
A: The area of the triangle equals the product of the semi-perimeter and the inradius (Area = r × s, where s is the semi-perimeter).

Q4: Can I calculate inradius for any type of triangle?
A: Yes, this formula works for all types of triangles (acute, obtuse, right, equilateral, isosceles, scalene).

Q5: What's the difference between inradius and circumradius?
A: Inradius is the radius of the inscribed circle (inside the triangle), while circumradius is the radius of the circumscribed circle (outside the triangle passing through all vertices).