The perpendicular offset from the junction of a transition curve and a circular curve to the tangent is a crucial concept in highway design. This offset relates to the "shift" of the curve, which is the lateral displacement required for the transition curve to connect smoothly between a straight tangent line and a circular curve.
For transition curves, the shift (denoted as "S") is typically calculated using properties of the curve such as length and radius. The relation between the offset and the shift is derived through geometric considerations and the dynamics of how a vehicle travels along these curves.
In this context, the perpendicular offset from the junction to the tangent is determined to be 4 times the shift. This is derived through geometric derivations in highway engineering, reflecting the requirement for smooth vehicular motion and safety.
Therefore, the correct option is: 4 times shift.