For a chord of 60 m, the mid-ordinate for a circular curve of 50 m radius will be
- A10 mCorrect
- B12.5 m
- C15 m
- D18.75 m
Solution
Concept
Mid-ordinate (versine) of a chord
Formula
M = R − √(R² − (C/2)²)
Step-by-step solution
1. R = 50 m, chord C = 60 m so C/2 = 30 m. 2. √(R² − 30²) = √(2500 − 900) = 40 m. 3. M = 50 − 40 = 10 m.
Explanation
The mid-ordinate is the distance between the middle of the chord and the middle of the arc. With a 3-4-5 triangle (30, 40, 50) it comes to 10 m.
Shortcut
3-4-5 triangle: half chord 30, radius 50, centre distance 40.
Common mistake
Using the full chord 60 instead of half the chord.
Correct answer: A) 10 m