GATE 2025 CE (CE1) – Question 35

Transportation Infrastructure · Geometric design of roadways: cross-section, sight distance, alignments · 1 mark · Numerical answer

Road A and Road B are joined by a circular horizontal curve of radius 200 m as shown in the figure. Road A and Road B are tangential to the curve at the points C and D, respectively. Had the curve not been there, straight roads A and B would have met at the point E. The distance from C to E is 92 m. The value of angle $\theta$ (in degrees) is ______________ (*rounded off to 1 decimal place*).

Note: The value of angle $\theta$ is to be calculated only from the consideration of Euclidean geometry and the data given in the problem.

Road A runs up to the point C, a circular curve joins C to D, and Road B runs on from D. The tangents at C and D, drawn dashed, meet at E. The angle $\theta$ is marked at E between the extension of the line CE and the line ED.

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Show answer and explanation

Correct answer: 49.15 to 49.65

Explanation

The tangent length is $CE = R\tan\frac{\theta}{2}$, where $\theta$ is the deflection angle, the angle between the extension of road A beyond E and road B. So $\tan\frac{\theta}{2} = \frac{92}{200} = 0.46$, $\frac{\theta}{2} = 24.7^\circ$ and $\theta = 49.4^\circ$.