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 can be calculated from the perimeter using a specific formula.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Isosceles Right Triangle (m)
• \( P \) — Perimeter of Isosceles Right Triangle (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula derives from the relationship between the perimeter and the circumradius in an isosceles right triangle, where the hypotenuse serves as the diameter of the circumcircle.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry and various engineering applications where circular properties of triangular shapes need to be determined, such as in construction and design.

4. Using the Calculator

Tips: Enter the perimeter of the isosceles right triangle in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a right triangle with two equal legs, making the angles 45°, 45°, and 90°.

Q2: How is the circumradius related to the triangle's sides?
A: In a right triangle, the circumradius is equal to half the length of the hypotenuse.

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 circumradius formulas.

Q4: What are practical applications of circumradius calculation?
A: Circumradius calculations are used in architecture, engineering, computer graphics, and various geometric design applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula. The calculator provides results with 6 decimal places for practical precision.