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. It represents the distance from the triangle's circumcenter to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula establishes the mathematical relationship between the circumradius and inradius of an isosceles right triangle, using the properties of square roots and geometric ratios.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry for understanding the properties of triangles, designing circular patterns around triangular shapes, and solving various geometric problems involving circumscribed circles.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding circumradius using the established mathematical relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between circumradius and inradius?
A: Circumradius is the radius of the circle circumscribed around the triangle (passing through all vertices), while inradius is the radius of the circle inscribed within the triangle (touching all sides).

Q2: 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 circumradius and inradius.

Q3: What are the practical applications of circumradius calculation?
A: Circumradius calculations are used in architecture, engineering design, computer graphics, and various fields where geometric properties of triangles need to be determined.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, though the displayed result may be rounded for practical purposes. The underlying formula is derived from geometric principles.

Q5: What units should be used for input?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system (inches, centimeters, etc.) as long as both input and output use the same units.