Circumradius of Right Angled Triangle Given Sides Calculator

Circumradius Formula:

\[ r_c = \frac{\sqrt{h^2 + B^2}}{2} \]

Circumradius of Right Angled Triangle:

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1. What is the Circumradius of Right Angled Triangle?

The Circumradius of Right Angled Triangle is the radius of a circumcircle touching each of the vertices of the Right-Angled Triangle. It's an important geometric property that helps in understanding the spatial relationships of the triangle.

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

\[ r_c = \frac{\sqrt{h^2 + B^2}}{2} \]

Where:

\( r_c \) — Circumradius of Right Angled Triangle (m)
\( h \) — Height of Right Angled Triangle (m)
\( B \) — Base of Right Angled Triangle (m)

Explanation: The formula calculates the radius of the circle that passes through all three vertices of the right-angled triangle, which is exactly half the length of the hypotenuse.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, engineering, and architecture for designing circular structures and understanding the spatial properties of right-angled triangles.

4. Using the Calculator

Tips: Enter the height and base of the right-angled triangle in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the circumradius half the hypotenuse in a right triangle?
A: In a right triangle, the hypotenuse is the diameter of the circumcircle, making the circumradius exactly half the length of the hypotenuse.

Q2: Does this formula work for all triangles?
A: No, this specific formula applies only to right-angled triangles. Other triangle types have different circumradius formulas.

Q3: What units should I use for the inputs?
A: The calculator uses meters, but the formula works with any consistent unit of measurement (cm, mm, inches, etc.).

Q4: Can the circumradius be larger than the triangle's sides?
A: Yes, the circumradius can be larger than the triangle's sides, especially in acute triangles, but in right triangles it's always exactly half the hypotenuse.

Q5: How is this different from the inradius?
A: The circumradius is the radius of the circle passing through all vertices, while the inradius is the radius of the circle tangent to all three sides.