1. What is the Inradius of a Triangle?

The inradius of a triangle is the radius of the circle inscribed within the triangle that 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 Heron's formula to calculate the inradius:

Where:

• \( r_i \) — Inradius of the triangle
• \( s \) — Semiperimeter of the triangle (\( s = \frac{S_a + S_b + S_c}{2} \))
• \( S_a \) — 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: The formula calculates the area of the triangle using Heron's formula and then divides it by the semiperimeter to find the inradius.

3. Importance of Inradius Calculation

Details: The inradius is important in geometry for determining properties of triangles, calculating areas of inscribed circles, 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 that satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between inradius and area?
A: The area of a triangle equals the product of its semiperimeter and inradius (Area = s × r_i).

Q2: Can any triangle have an inscribed circle?
A: Yes, every triangle has a unique inscribed circle (incircle) tangent to all three sides.

Q3: How does inradius relate to triangle type?
A: Equilateral triangles have the maximum possible inradius for a given perimeter, while very elongated triangles have smaller inradii.

Q4: What are the limitations of this calculation?
A: The formula only works for valid triangles where the sum of any two sides is greater than the third side.

Q5: Can I use different units of measurement?
A: Yes, but all sides must use the same unit, and the result will be in that same unit.