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Chord Length of Quarter Circle Formula:
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The chord length of a quarter circle is the length of the straight line that connects the two endpoints of the quarter circle's arc. It represents the longest distance between any two points on the quarter circle's circumference.
The calculator uses the chord length formula:
Where:
Explanation: The formula is derived from the Pythagorean theorem applied to the right triangle formed by the radius and chord in a quarter circle.
Details: Calculating chord length is essential in geometry, engineering, and architecture for determining distances, designing curved structures, and solving spatial problems involving circular segments.
Tips: Enter the radius of the quarter circle in meters. The value must be positive and valid. The calculator will compute the chord length using the mathematical formula.
Q1: Why is the chord length formula r×√2?
A: In a quarter circle, the chord forms the hypotenuse of a right triangle with two equal sides (both equal to the radius), so by Pythagorean theorem: chord = √(r² + r²) = r√2.
Q2: Does this formula work for any quarter circle?
A: Yes, this formula applies to all quarter circles regardless of size, as long as it's a perfect quarter of a circle.
Q3: What units should I use for the radius?
A: You can use any consistent unit (meters, centimeters, inches, etc.), but the calculator displays results in meters by default.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise value of √2. The calculator provides results with 6 decimal places for practical accuracy.
Q5: Can this formula be used for other circular segments?
A: No, this specific formula applies only to quarter circles. Other circular segments have different chord length formulas based on their central angles.