Once the alignment of a route is finalized, such as AVCD in Figure 37.1, the change in direction is achieved through provision of circular curves. In Figure 37.1, to change the direction from AV to VC, a circular curve T₁ GT₂ is provided. Similarly, from VC to CD, T'₁G'T'₂ is provided. The straight alignments, between which a curve is provided, are tangential to the curve. Thus, AT₁ V and VT₂C are tangential to T₁ GT₂ . The tangent line before the beginning of the curve is called the Back tangent or the rear tangent. The tangent line after the end of the curve is called the Forward tangent . The line AT₁ is the back tangent and the line T₂C is the forward tangent for the curve T₁GT₂. The distinction of the back tangent from the forward tangent depends on the direction of the route surveying. The point at which extension of the back tangent and the forward tangent meet is known as the Vertex (V) or point of intersection (P.I.). The exterior angle at the vertex or point of intersection is known as the Intersection angle (I). It is also known as Deflection angle (D) as it represents the deflection angle between the back tangent and the forward tangent. Thus, angle between the line AV produced beyond the vertex V and the line VC represents I (or D). The point on the back tangent where the curve begins is known as the Point of Curvature (P.C.). At this point, the alignment of the route changes from a straight line to a curve. This is represented by T₁ in Figure 37.1. The point on the forward tangent where the curve ends is known as the Point of tangency (P.T.). At this point, the alignment of the route changes from a curve to a straight line. It is represented by T₂ in Figure 37.1. The distance between the point of curvature (T₁) to the point of intersection (V) along the extension of back tangent is known as Tangent distance (T). It is also equal to the distance between the point of tangency (T₂) to the point of intersection along the extension of forward tangent. The distance between the point of intersection (V) and the middle point of the curve is called as External distance (E). The longest possible chord of the circular curve is known as Long chord (L). It is the line joining the point of curvature (T₁) and the point of tangency (T₂). The distance between the middle point of the curve and the middle point of the long chord is Mid-ordinate (M). The length of the alignment along the curve between the point of curvature (T₁) and the point of tangency (T₂) is known as the Length of curve (l). During the progress of the route, if the direction of deflection is to the right then it is called Right-hand curve (T₁GT₂) and it is called left -hand curve, if the curve deflects to the left T'₁G'T'₂.

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