1. What is the Circumradius of Isosceles Right Triangle?

The circumradius of an isosceles right triangle is the radius of the circumscribed circle that passes through all three vertices of the triangle. For an isosceles right triangle, this radius equals half the length of the hypotenuse.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Isosceles Right Triangle (m)
• \( H \) — Hypotenuse of Isosceles Right Triangle (m)

Explanation: In an isosceles right triangle, the hypotenuse serves as the diameter of the circumscribed circle, making the circumradius exactly half of the hypotenuse length.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry for understanding the properties of triangles and their circumscribed circles. It has applications in various fields including engineering, architecture, and computer graphics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the circumradius exactly half the hypotenuse?
A: In a right triangle, the hypotenuse is always the diameter of the circumscribed circle (Thales' theorem), making the circumradius half of the hypotenuse length.

Q2: Does this formula work for all right triangles?
A: Yes, this formula applies to all right triangles, not just isosceles ones. The circumradius of any right triangle equals half the hypotenuse length.

Q3: What are the units for circumradius?
A: The circumradius has the same units as the hypotenuse input (typically meters, but could be any length unit).

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for precise calculations.

Q5: What if I have the leg lengths instead of hypotenuse?
A: First calculate the hypotenuse using Pythagorean theorem (H = √(a² + a²) = a√2 for isosceles right triangle), then use this calculator.