1. What is Inradius of Isosceles Right Triangle?

The inradius of an isosceles right triangle is the radius of the largest circle that can fit inside the triangle, tangent to all three sides. It represents the distance from the triangle's incenter to any of its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Circumradius \) — The radius of the circle passing through all three vertices of the triangle
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes the relationship between the circumradius (radius of the circumscribed circle) and the inradius (radius of the inscribed circle) in an isosceles right triangle.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which has applications in various fields including engineering, architecture, and design where circular elements need to fit within triangular spaces.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding inradius of the isosceles right triangle.

5. Frequently Asked Questions (FAQ)

Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a triangle with two equal sides and one right angle (90 degrees). The two equal sides are the legs, and the third side is the hypotenuse.

Q2: How is circumradius related to inradius in this triangle?
A: In an isosceles right triangle, the circumradius is exactly \( (1 + \sqrt{2}) \) times larger than the inradius.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to isosceles right triangles. Other triangle types have different relationships between their circumradius and inradius.

Q4: What are practical applications of this calculation?
A: This calculation is useful in geometric design, construction planning, and any application where circular elements need to be precisely placed within triangular spaces.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though the result may be rounded for practical purposes. The accuracy depends on the precision of the input value.