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The Angle of Circular Arc is the angle subtended by the end points of a Circular Arc with the center of the circle from which the arc is formed. It represents the measure of the arc in angular units.
The calculator uses the formula:
Where:
Explanation: This formula demonstrates the fundamental relationship between an inscribed angle and the corresponding central angle in a circle, where the central angle is always twice the measure of the inscribed angle that subtends the same arc.
Details: Calculating arc angles is essential in geometry, engineering, and various technical fields where circular measurements are required. It helps in determining arc lengths, sector areas, and understanding circular motion properties.
Tips: Enter the inscribed angle in radians. The value must be positive and greater than zero. The calculator will compute the corresponding arc angle using the formula ∠Arc = 2 × ∠Inscribed.
Q1: What is the relationship between inscribed angle and central angle?
A: The central angle (arc angle) is always twice the measure of any inscribed angle that subtends the same arc.
Q2: Can this formula be used for angles in degrees?
A: Yes, the relationship holds true regardless of the angular unit, as long as both angles use the same unit of measurement.
Q3: Does this formula work for all types of circles?
A: Yes, this is a fundamental property of Euclidean geometry that applies to all circles.
Q4: What are some practical applications of this calculation?
A: This calculation is used in architecture, mechanical engineering, navigation, and various fields involving circular design and measurements.
Q5: Is there any limitation to this formula?
A: The formula assumes a perfect circle and applies only when the inscribed angle and central angle subtend the same arc of the circle.