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The radius of a quarter circle can be determined from its chord length using a specific geometric relationship. This calculation is essential in various geometric and engineering applications where quarter circle properties are involved.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric relationship between the chord (which is the hypotenuse of the right triangle formed by the two radii) and the radius in a quarter circle.
Details: Calculating the radius from chord length is crucial in architectural design, mechanical engineering, and various geometric constructions where quarter circle segments are used.
Tips: Enter the chord length in meters. The value must be valid (greater than 0). The calculator will compute the corresponding radius of the quarter circle.
Q1: Why is there a square root of 2 in the denominator?
A: The square root of 2 appears because the chord forms the hypotenuse of a right isosceles triangle with the two radii as legs.
Q2: Can this formula be used for full circles?
A: No, this specific formula applies only to quarter circles where the chord connects the endpoints of the arc.
Q3: What are typical applications of this calculation?
A: This calculation is used in architectural design, mechanical part design, and geometric constructions involving circular segments.
Q4: How accurate is this formula?
A: The formula is mathematically exact and provides precise results for perfect quarter circles.
Q5: What units should be used for input?
A: While meters are shown as default, any consistent length unit can be used (cm, mm, inches, etc.) as long as the same unit is used throughout.