To find the stationing of the Point of Intersection (P.I.), we need to calculate the chord length and determine the stationing from the given data.

Data Given:

1. Offset distance from P.C. to P.T.: $d = 20 \, \text{m}$
2. Intersection angle: $I = 32^\circ$
3. Stationing of P.T.: $\text{Sta}_{PT} = 10 + 256.32$
   • Converting $\text{Sta}_{PT}$: $10 + 256.32 = 10256.32 \, \text{m}$.

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Step 1: Relationship between offset, chord, and intersection angle

The relationship between the offset $d$, chord $C$, and intersection angle $I$ is given by: $d = \frac{C}{2} \tan \frac{I}{2}$

Rearranging for $C$, the chord length: $C = 2d \cot \frac{I}{2}$

Substitute the values:

• $d = 20 \, \text{m}$,
• $\frac{I}{2} = \frac{32^\circ}{2} = 16^\circ$.

Using $\cot$: $C = 2 \cdot 20 \cdot \cot(16^\circ)$

Calculate: $\cot(16^\circ) \approx 3.487$ $C = 2 \cdot 20 \cdot 3.487 = 139.48 \, \text{m}$

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Step 2: Stationing of P.I.

The stationing of P.I. can be calculated as: $\text{Sta}_{PI} = \text{Sta}_{PT} - C$

Substitute the values: $\text{Sta}_{PI} = 10256.32 - 139.48 = 10116.84 \, \text{m}$

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Final Answer:

The stationing of the P.I. is: $\boxed{10 + 116.84}$

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Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How is the offset distance related to the curve's radius and angle?
2. What if the offset distance or intersection angle changes—how would it affect the chord length?
3. How can we calculate the radius of the curve if needed?
4. How is the curve's deflection angle computed from such data?
5. What is the significance of stationing in horizontal curve alignment?

Tip: Always double-check your trigonometric functions and angle conversions to ensure accurate calculations.