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Chord Length of Quarter Circle Formula:
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The Chord Length of Quarter Circle is the length of the line joining the two radii of the Quarter Circle. It represents the straight line distance between the two endpoints of the quarter circle's arc.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric properties of a quarter circle, where the chord length forms the hypotenuse of a right isosceles triangle with legs equal to the radius.
Details: Calculating chord length is essential in various geometric and engineering applications, particularly in circular segment analysis, arch design, and circular construction projects where precise measurements are required.
Tips: Enter the diameter of the circle from which the quarter circle is cut. The value must be positive and measured in meters. The calculator will automatically compute the chord length.
Q1: Why is the formula divided by √2?
A: The √2 factor comes from the Pythagorean theorem applied to the right isosceles triangle formed by the chord and the two radii.
Q2: Can this formula be used for other circular segments?
A: This specific formula applies only to quarter circles. Other circular segments require different formulas based on their central angles.
Q3: What's the relationship between chord length and arc length?
A: For a quarter circle, the chord length is shorter than the arc length. The arc length is πD/4 while the chord length is D/√2.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect quarter circles. Real-world applications may require considering material properties and construction tolerances.
Q5: Can this be used for diameter calculation from chord length?
A: Yes, the formula can be rearranged to calculate diameter from chord length: D = lChord × √2.