What is the relationship between the deflection angle and the central angle?

• A. The deflection angle is equal to the central angle
• B. The deflection angle is half of the central angle
• C. The deflection angle is double the central angle
• D. The deflection angle varies independently of the central angle

Answer: (C)

The relationship between the deflection angle and the central angle is based on geometric principles in circles, particularly in the context of circular arcs used in road design and surveying. The central angle is defined as the angle subtended at the center of the circle by two radii terminating at the circumference, while the deflection angle is formed by two tangents at the endpoints of that arc.

In a circular path, the deflection angle is indeed double the central angle. This is because when you look at the arc from the center of the circle, the angle that forms between the radii will always be half of the angle created between the tangents at the ends of that arc. This relationship allows engineers and surveyors to calculate alignments and offsets effectively, using straightforward trigonometric principles. Understanding this relationship is crucial when designing curves in roads, as it helps determine the necessary adjustments for safe vehicle navigation.

The other provided options do not reflect this geometric truth: the deflection angle does not simply equal the central angle, nor is it half of it. Additionally, stating that the deflection angle varies independently of the central angle contradicts the inherent geometric relationships at play, as the two angles are directly related by this doubling effect.