Curve Geometry – Definition of Angle of Intersection (I) In highway/railway curve terminology, the angle of intersection I is defined as the angle between which pair of lines at the point of intersection (PI)?

Introduction / Context:
Simple circular curves are defined with respect to tangents that meet at the Point of Intersection (PI). The “angle of intersection” I directly controls several layout elements such as tangent length, external distance, and degree of curve. Precise definition prevents confusion during design and field layout.

Given Data / Assumptions:

• Back and forward tangents are straight lines meeting at the PI when extended appropriately.
• Long chord connects points of tangency, not necessarily passing through the PI.
• Standard curve geometry conventions apply.

Concept / Approach:

The angle of intersection I is the included angle between the two tangents at the PI. In phrasing, this is often stated as the angle between the prolongation of the back tangent and the forward tangent. This definition underlies formulas such as tangent length T = R * tan(I / 2) and long chord LC = 2 * R * sin(I / 2).

Step-by-Step Solution:

Verification / Alternative check:

Substituting I into standard formulas reproduces correct curve elements; using long chords instead of tangents would not yield those relations, confirming the proper definition.

Why Other Options Are Wrong:

(a) is imprecise unless one explicitly states “at their intersection when prolonged”; (c) and (d) involve chords, not the defining tangents; (e) is not a standard definition.

Common Pitfalls:

Confusing angle at the PI with central angle at the circle’s center; mixing up “external distance” and “mid-ordinate” formulas.

Final Answer:

Prolongation of the back tangent and the forward tangent