[Directions: The chainage of the intersection point of two straights is 1060 m, and the angle of intersection is 120°. If radius of a circular curve to be set out is 570 m, and peg interval is 30 m.] What is the length of the long chord?
- A370 m
- B470 m
- C670 m
- D570 mCorrect
Solution
Concept
Long chord = 2R sin(Δ/2), where Δ is the deflection angle.
Formula
Lc = 2R sin(Δ/2); Δ = 180° − I
Step-by-step solution
1. Deflection angle Δ = 180° − 120° = 60°. 2. Δ/2 = 30°, and sin 30° = 0.5. 3. Lc = 2 × 570 × 0.5. 4. Lc = 570 m.
Explanation
The long chord joins the two tangent points (T1 and T2). Its length is 2R sin(Δ/2). With Δ = 60°, the chord equals the radius, 570 m.
Why the other options are wrong
370 m, 470 m and 670 m do not match 2R sin 30° = 570 m. Using Δ = 120° would give 987 m, which is not an option.
Shortcut
When Δ = 60°, the long chord equals R (an equilateral triangle forms with the centre).
Common mistake
Taking Δ = 120° (the angle of intersection) instead of 60°.
Correct answer: D) 570 m