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Circumradius of Isosceles Right Triangle Formula:
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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 center of the circumcircle to any vertex of the triangle.
The calculator uses the circumradius formula:
Where:
Explanation: The formula derives from the geometric properties of an isosceles right triangle, where the hypotenuse equals \( S_{Legs} \times \sqrt{2} \), and in a right triangle, the circumradius equals half the hypotenuse.
Details: Calculating the circumradius is important in geometry for understanding the circumscribed circle properties of isosceles right triangles, which has applications in various fields including engineering, architecture, and computer graphics.
Tips: Enter the length of the legs of the isosceles right triangle in meters. The value must be positive and greater than zero.
Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a right triangle with two equal legs and angles of 45°, 45°, and 90°.
Q2: Why is the circumradius half the hypotenuse?
A: In any right triangle, the circumcenter lies at the midpoint of the hypotenuse, making the circumradius equal to half the length of the hypotenuse.
Q3: How is this formula derived?
A: The hypotenuse = \( S_{Legs} \times \sqrt{2} \), and circumradius = hypotenuse/2 = \( S_{Legs}/\sqrt{2} \).
Q4: 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.
Q5: What are practical applications of circumradius calculation?
A: Applications include designing circular components that circumscribe triangular shapes, architectural planning, and geometric modeling in various engineering fields.